List of Mathematical Constants

8/10/2019 List of Mathematical Constants

1/25

Mathematical Constants

a selection compiled byStanislav Skora,Extra Byte,Castano Primo, Italy.Stan's Library,Ed.S.Sykora, Vol.II. First release March 31, 2008. Permalink via DOI:10.3247/SL2Math08.001

This page is dedicated to my late teacher Jaroslav Bayerwho, back in 1955-8, kindled my passion for Mathematics.

Math LINKS|SI Units|Dimensions of various quantities PHYSICS Constants(on a separate page) Science LINKS|Stan's Library|Stan's HUB

This is a constant-at-a-glancelist. It keeps growing, so keep coming back.Bold dots after a valueare links to the OEIS database.

Basic mathematical constants ...

... and those derived from them

Classical named math constants

Other notable math constants

Notable integer numbers

Notable integer sequences

Rational numbers and sequences

Function-related constants

Geometry constants

Statistics / probability constants

Constants useful in Sciences

Engineering constants

Software engineering constants

Conversion constants

Notes,ReferencesandLinks

Basic math constants

Zero and One(and i, and ...) 0 and 1 (and (-1), and ...) Can anything be more basic than these two ? (or three, or ...)

,Archimedes' constant 3.141 592 653 589 793 238 462 643 Circumference of a disc with unit diameter.

e,Euler number,Napier's constant 2.718 281 828 459 045 235 360 287 Base of natural logarithms.

,Euler-Mascheroni constant 0.577 215 664 901 532 860 606 512 Limit[n]{(1+1/2+1/3+...1/n) - ln(n)}

2,Pythagora's constant 1.414 213 562 373 095 048 801 688 Diagonal of a square with unit side.

,Golden ratio 1.618 033 988 749 894 848 204 586 = (5 + 1)/2 = 2.cos(/5). Diagonal of a unit side pentagon.

, Inverse golden ratio(often confused with ) 0.618 033 988 749 894 848 204 586 = 1/ = -1 =(1-)/ or = (5 - 1)/2.

s,Silver ratio / mean

2.414 213 562 373 095 048 801 688

s= 1+2.

Constants derived from the basic ones

Conversions between logarithmsfor bases 2, e, 10:

ln(2), Natural logarithm of 2 0.693 147 180 559 945 309 417 232 ex= 2
mailto:[email protected]:[email protected]:[email protected]://www.ebyte.it/index.htmlhttp://www.ebyte.it/index.htmlhttp://www.ebyte.it/index.htmlhttp://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/library/Library.htmlhttp://dx.doi.org/10.3247/SL2Math08.001http://dx.doi.org/10.3247/SL2Math08.001http://dx.doi.org/10.3247/SL2Math08.001http://www.ebyte.it/library/StansMathLinks.htmlhttp://www.ebyte.it/library/StansMathLinks.htmlhttp://www.ebyte.it/library/educards/siunits/TablesOfSiUnitsAndPrefixes.htmlhttp://www.ebyte.it/library/educards/siunits/TablesOfSiUnitsAndPrefixes.htmlhttp://www.ebyte.it/library/educards/siunits/TablesOfSiUnitsAndPrefixes.htmlhttp://www.ebyte.it/library/educards/sidimensions/SiDimensionsByCategory.htmlhttp://www.ebyte.it/library/educards/sidimensions/SiDimensionsByCategory.htmlhttp://www.ebyte.it/library/educards/sidimensions/SiDimensionsByCategory.htmlhttp://www.ebyte.it/library/educards/constants/ConstantsOfPhysicsAndMath.htmlhttp://www.ebyte.it/library/educards/constants/ConstantsOfPhysicsAndMath.htmlhttp://www.ebyte.it/library/StansLinks.htmlhttp://www.ebyte.it/library/StansLinks.htmlhttp://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/index.htmlhttp://www.ebyte.it/index.htmlhttp://www.ebyte.it/index.htmlhttp://oeis.org/http://oeis.org/http://oeis.org/http://www.ebyte.it/library/educards/constants/MathConstants.html#basichttp://www.ebyte.it/library/educards/constants/MathConstants.html#basichttp://www.ebyte.it/library/educards/constants/MathConstants.html#derivedhttp://www.ebyte.it/library/educards/constants/MathConstants.html#derivedhttp://www.ebyte.it/library/educards/constants/MathConstants.html#classicalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#classicalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#otherhttp://www.ebyte.it/library/educards/constants/MathConstants.html#otherhttp://www.ebyte.it/library/educards/constants/MathConstants.html#integerhttp://www.ebyte.it/library/educards/constants/MathConstants.html#integerhttp://www.ebyte.it/library/educards/constants/MathConstants.html#intseqhttp://www.ebyte.it/library/educards/constants/MathConstants.html#intseqhttp://www.ebyte.it/library/educards/constants/MathConstants.html#rationalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#rationalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#usefulhttp://www.ebyte.it/library/educards/constants/MathConstants.html#usefulhttp://www.ebyte.it/library/educards/constants/MathConstants.html#geometryhttp://www.ebyte.it/library/educards/constants/MathConstants.html#geometryhttp://www.ebyte.it/library/educards/constants/MathConstants.html#statisticshttp://www.ebyte.it/library/educards/constants/MathConstants.html#statisticshttp://www.ebyte.it/library/educards/constants/MathConstants.html#mathphyshttp://www.ebyte.it/library/educards/constants/MathConstants.html#mathphyshttp://www.ebyte.it/library/educards/constants/MathConstants.html#engineeringhttp://www.ebyte.it/library/educards/constants/MathConstants.html#engineeringhttp://www.ebyte.it/library/educards/constants/MathConstants.html#softdevhttp://www.ebyte.it/library/educards/constants/MathConstants.html#softdevhttp://www.ebyte.it/library/educards/constants/MathConstants.html#conversionhttp://www.ebyte.it/library/educards/constants/MathConstants.html#conversionhttp://www.ebyte.it/library/educards/constants/MathConstants.html#noteshttp://www.ebyte.it/library/educards/constants/MathConstants.html#noteshttp://www.ebyte.it/library/educards/constants/MathConstants.html#refshttp://www.ebyte.it/library/educards/constants/MathConstants.html#refshttp://www.ebyte.it/library/educards/constants/MathConstants.html#refshttp://www.ebyte.it/library/educards/constants/MathConstants.html#linkshttp://www.ebyte.it/library/educards/constants/MathConstants.html#linkshttp://www.ebyte.it/library/educards/constants/MathConstants.html#linkshttp://mathworld.wolfram.com/Pi.htmlhttp://mathworld.wolfram.com/Pi.htmlhttp://mathworld.wolfram.com/Pi.htmlhttps://oeis.org/A000796https://oeis.org/A000796https://oeis.org/A000796http://en.wikipedia.org/wiki/E_(mathematical_constant)http://en.wikipedia.org/wiki/E_(mathematical_constant)http://en.wikipedia.org/wiki/E_(mathematical_constant)https://oeis.org/A001113https://oeis.org/A001113https://oeis.org/A001113http://mathworld.wolfram.com/Euler-MascheroniConstant.htmlhttp://mathworld.wolfram.com/Euler-MascheroniConstant.htmlhttp://mathworld.wolfram.com/Euler-MascheroniConstant.htmlhttps://oeis.org/A001620https://oeis.org/A001620https://oeis.org/A001620http://mathworld.wolfram.com/PythagorassConstant.htmlhttp://mathworld.wolfram.com/PythagorassConstant.htmlhttp://mathworld.wolfram.com/PythagorassConstant.htmlhttps://oeis.org/A002193https://oeis.org/A002193https://oeis.org/A002193http://en.wikipedia.org/wiki/Golden_ratiohttp://en.wikipedia.org/wiki/Golden_ratiohttp://en.wikipedia.org/wiki/Golden_ratiohttps://oeis.org/A001622https://oeis.org/A001622https://oeis.org/A001622https://oeis.org/A094214https://oeis.org/A094214https://oeis.org/A094214http://en.wikipedia.org/wiki/Silver_ratiohttp://en.wikipedia.org/wiki/Silver_ratiohttp://en.wikipedia.org/wiki/Silver_ratiohttps://oeis.org/A014176https://oeis.org/A014176https://oeis.org/A014176http://oeis.org/A002162http://oeis.org/A002162http://oeis.org/A002162http://oeis.org/A002162https://oeis.org/A014176http://en.wikipedia.org/wiki/Silver_ratiohttps://oeis.org/A094214https://oeis.org/A001622http://en.wikipedia.org/wiki/Golden_ratiohttps://oeis.org/A002193http://mathworld.wolfram.com/PythagorassConstant.htmlhttps://oeis.org/A001620http://mathworld.wolfram.com/Euler-MascheroniConstant.htmlhttps://oeis.org/A001113http://en.wikipedia.org/wiki/E_(mathematical_constant)https://oeis.org/A000796http://mathworld.wolfram.com/Pi.htmlhttp://www.ebyte.it/library/educards/constants/MathConstants.html#linkshttp://www.ebyte.it/library/educards/constants/MathConstants.html#refshttp://www.ebyte.it/library/educards/constants/MathConstants.html#noteshttp://www.ebyte.it/library/educards/constants/MathConstants.html#conversionhttp://www.ebyte.it/library/educards/constants/MathConstants.html#softdevhttp://www.ebyte.it/library/educards/constants/MathConstants.html#engineeringhttp://www.ebyte.it/library/educards/constants/MathConstants.html#mathphyshttp://www.ebyte.it/library/educards/constants/MathConstants.html#statisticshttp://www.ebyte.it/library/educards/constants/MathConstants.html#geometryhttp://www.ebyte.it/library/educards/constants/MathConstants.html#usefulhttp://www.ebyte.it/library/educards/constants/MathConstants.html#rationalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#intseqhttp://www.ebyte.it/library/educards/constants/MathConstants.html#integerhttp://www.ebyte.it/library/educards/constants/MathConstants.html#otherhttp://www.ebyte.it/library/educards/constants/MathConstants.html#classicalhttp://www.ebyte.it/library/educards/constants/MathConstants.html#derivedhttp://www.ebyte.it/library/educards/constants/MathConstants.html#basichttp://oeis.org/http://www.ebyte.it/index.htmlhttp://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/library/StansLinks.htmlhttp://www.ebyte.it/library/educards/constants/ConstantsOfPhysicsAndMath.htmlhttp://www.ebyte.it/library/educards/sidimensions/SiDimensionsByCategory.htmlhttp://www.ebyte.it/library/educards/siunits/TablesOfSiUnitsAndPrefixes.htmlhttp://www.ebyte.it/library/StansMathLinks.htmlhttp://dx.doi.org/10.3247/SL2Math08.001http://www.ebyte.it/library/Library.htmlhttp://www.ebyte.it/index.htmlmailto:[email protected]


2/25

log(2), Decadic logarithm of 2 0.301 029 995 663 981 195 213 738 10x= 2

ln(10), Natural logarithm of 10 2.302 585 092 994 045 684 017 991 ex= 10

ln2(10), Binary logarithm of 10 3.321 928 094 887 362 347 870 319 2x= 10

log(e), Decadic logarithm of e 0.434 294 481 903 251 827 651 128 10x= e

ln2(e), Binary logarithm of e 1.442 695 040 888 963 407 359 924 2x= e

Spin-offs of the imaginary unit i. Formally, iis a solution of z2= -1 and of z = e z/2. For any integer k and any z, i4k+z= iz. i4f= ei2f

De Moivre numbersei2k/n cos(2k/n) +i.sin(2k/n) for any integer k and n0.

ii= e-/2, the imaginary unit elevated to itself 0.207 879 576 350 761 908 546 955 A transcendental real number

i-i= (-1)-i/2= e/2 4.810 477 380 965 351 655 473 035 Inverse of the above. Square root of Gelfond's constant.

ln(i) / i= /2 1.570 796 326 794 896 619 231 321 This value could also be classified as a spin-off

i!= (1+i) = i*(i) (see Gamma function) 0.498 015 668 118 356 042 713 691 -i0.154 949 828 301 810 685 124 955

| i!| absolute value of the above 0.521 564 046 864 939 841 158 180 arg( i!) = - 0.301 640 320 467 533 197 887 531rad

iîî^... infinite power tower of i; solution of z = iz 0.438 282 936 727 032 111 626 975 +i0.360 592 471 871 385 485 952 940

| iîî| absolute value of the above 0.567 555 163 306 957 825 384 613 arg( iîî^...) = 0.688 453 227 107 702 130 498 767rad

Basic roots of i, up to a term of 4k in the exponent (like i4k+1/4= i1/4, for any integer k):

i1/2= i= (1 + i)/2 = cos(/4) +i.sin(/4) 0.707 106 781 186 547 524 400 844 +i0.707 106 781 186 547 524 400 844

i1/3= (3 +i)/2 = cos(/6) +i.sin(/6) 0.866 025 403 784 438 646 763 723 +i0.5

i1/4= cos(/8) +i.sin(/8) 0.923 879 532 511 286 756 128 183 +i0.382 683 432 365 089 771 728 459

i1/5= cos(/10) +i.sin(/10) 0.951 056 516 295 153 572 116 439 +i0.309 016 994 374 947 424 102 293

i1/6= cos(/12) +i.sin(/12) 0.965 925 826 289 068 2867 497 431 +i0.258 819 045 102 520 762 348 898

i1/7

= cos(/14) +i.sin(/14)

0.974 927 912 181 823 607 018 131

+i0.222 520 933 956 314 404 288 902

i1/8= cos(/16) +i.sin(/16) 0.980 785 280 403 230 449 126 182 +i0.195 090 322 016 128 267 848 284

i1/9= cos(/18) +i.sin(/18) 0.984 807 753 012 208 059 366 743 +i0.173 648 177 666 930 348 851 716

i1/10= cos(/20) +i.sin(/20) 0.987 688 340 595 137 726 190 040 +i0.156 434 465 040 230 869 010 105

e spin-of fs; note also that PowerTower(e1/e) = (e1/e)^(e1/e)^(e1/e)^... = e
http://oeis.org/A007524http://oeis.org/A007524http://oeis.org/A007524http://oeis.org/A002392http://oeis.org/A002392http://oeis.org/A002392http://oeis.org/A020862http://oeis.org/A020862http://oeis.org/A020862http://oeis.org/A002285http://oeis.org/A002285http://oeis.org/A002285http://oeis.org/A007525http://oeis.org/A007525http://oeis.org/A007525http://oeis.org/A049006http://oeis.org/A049006http://oeis.org/A049006https://oeis.org/A042972https://oeis.org/A042972https://oeis.org/A042972https://oeis.org/A019669https://oeis.org/A019669https://oeis.org/A019669https://oeis.org/A212877https://oeis.org/A212877https://oeis.org/A212877https://oeis.org/A212878https://oeis.org/A212878https://oeis.org/A212878https://oeis.org/A212879https://oeis.org/A212879https://oeis.org/A212879https://oeis.org/A212880https://oeis.org/A212880https://oeis.org/A212880http://oeis.org/A077589http://oeis.org/A077589http://oeis.org/A077589http://oeis.org/A077590http://oeis.org/A077590http://oeis.org/A077590http://oeis.org/A212479http://oeis.org/A212479http://oeis.org/A212479http://oeis.org/A212480http://oeis.org/A212480http://oeis.org/A212480http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A010527http://oeis.org/A010527http://oeis.org/A010527http://oeis.org/A144981http://oeis.org/A144981http://oeis.org/A144981http://oeis.org/A182168http://oeis.org/A182168http://oeis.org/A182168http://oeis.org/A019881http://oeis.org/A019881http://oeis.org/A019881http://oeis.org/A019827http://oeis.org/A019827http://oeis.org/A019827http://oeis.org/A019884http://oeis.org/A019884http://oeis.org/A019884http://oeis.org/A019824http://oeis.org/A019824http://oeis.org/A019824http://oeis.org/A232735http://oeis.org/A232735http://oeis.org/A232735http://oeis.org/A232736http://oeis.org/A232736http://oeis.org/A232736http://oeis.org/A232737http://oeis.org/A232737http://oeis.org/A232737http://oeis.org/A232738http://oeis.org/A232738http://oeis.org/A232738http://oeis.org/A019889http://oeis.org/A019889http://oeis.org/A019889http://oeis.org/A019819http://oeis.org/A019819http://oeis.org/A019819http://oeis.org/A019890http://oeis.org/A019890http://oeis.org/A019890http://oeis.org/A019818http://oeis.org/A019818http://oeis.org/A019818http://oeis.org/A019818http://oeis.org/A019890http://oeis.org/A019819http://oeis.org/A019889http://oeis.org/A232738http://oeis.org/A232737http://oeis.org/A232736http://oeis.org/A232735http://oeis.org/A019824http://oeis.org/A019884http://oeis.org/A019827http://oeis.org/A019881http://oeis.org/A182168http://oeis.org/A144981http://oeis.org/A010527http://oeis.org/A010503http://oeis.org/A010503http://oeis.org/A212480http://oeis.org/A212479http://oeis.org/A077590http://oeis.org/A077589https://oeis.org/A212880https://oeis.org/A212879https://oeis.org/A212878https://oeis.org/A212877https://oeis.org/A019669https://oeis.org/A042972http://oeis.org/A049006http://oeis.org/A007525http://oeis.org/A002285http://oeis.org/A020862http://oeis.org/A002392http://oeis.org/A007524


3/25

2e 5.436 563 656 918 090 470 720 574 1/e= 0.367 879 441 171 442 321 595 523

cosh(1) = (e + 1/e)/2 1.543 080 634 815 243 778 477 905 sinh(1) = (e - 1/e)/2 = 1.175 201 193 643 801 456 882 381

e2, conic constant or Schwarzschild constant 7.389 056 098 930 650 227 230 427 1/e2= 0.135 335 283 236 612 691 893 999

e 1.648 721 270 700 128 146 848 650 1/e= 0.606 530 659 712 633 423 603 799

ei= cos(1) isin(1) = cosh(i) sinh(i) 0.540 302 305 868 139 717 400 936 i0.841 470 984 807 896 506 652 502

ee 15.154 262 241 479 264 189 760 430 e-e= 0.065 988 035 845 312 537 0767 901

eie= cos(e) i.sin(e) - 0.911 733 914 786 965 097 893 717 i0.410 781 290 502 908 695 476 009

ie= cos(e/2) i.sin(e/2) -0.428 219 773 413 827 753 760 262 i-0.903 674 623 776 395 536 600 853

e1/e 1.444 667 861 009 766 133 658 339 e-1/e= 0.692 200 627 555 346 353 865 421

ei/e= cos(1/e) i.sin(1/e) 0.933 092 075 598 208 563 540 410 i0.359 637 565 412 495 577 0382 503

Infinite power tower of 1/e (Omega constant) 0.567 143 290 409 783 872 999 968 (1/e)^(1/e)^(1/e)^...; also solution of x = e -x

Ramanujan's number: 262537412640768743 + 0.999 999 999 999 250 072 597 198 exp(163). Closest approach of exp(n) to integer.

spin-offs

2 6.283 185 307 179 586 476 925 286 1/= 0.318 309 886 183 790 671 537 767

2 9.869 604 401 089 358 618 834 490 1/2= 0.101 321 183 642 337 771 443 879

1.772 453 850 905 516 027 298 167 1/= 0.564 189 583 547 756 286 948 079

ln() 1.144 729 885 849 400 174 143 427 log10() = 0.497 149 872 694 133 854 351 268

ln(). 3.596 274 999 729 158 198 086 001 ln()/= 0.364 378 839 675 906 257 049 587

36.462 159 607 207 911 770 990 826 -= 0.027 425 693 123 298 106 119 556

1/ 1.439 619 495 847 590 688 336 490 -1/= 0.694 627 992 246 826 153 124 383

i

= cos(ln()) i.sin(ln())

0.413 292 116 101 594 336 626 628

i0.910 598 499 212 614 707 060 044

i= cos(2/2) + i.sin(2/2) 0.220 584 040 749 698 088 668 945 - i0.975 367 972 083 631 385 157 482

i= cos(.ln()) i.sin(.ln()) -0.898 400 579 757 743 645 668 580 i-0.439 176 955 555 445 894 369 454

i/= cos(ln()/) i.sin(ln()/) 0.934 345 303 678 637 694 262 240 i0.356 368 985 033 313 899 907 691

e and combinations, except trivial ones like , for any integer k, e ik= (-1)k, cosh(ik) = (-1)k, sinh(ik) = 0
https://oeis.org/A019762https://oeis.org/A019762https://oeis.org/A019762https://oeis.org/A068985https://oeis.org/A068985https://oeis.org/A068985https://oeis.org/A073743https://oeis.org/A073743https://oeis.org/A073743https://oeis.org/A073742https://oeis.org/A073742https://oeis.org/A073742https://oeis.org/A072334https://oeis.org/A072334https://oeis.org/A072334https://oeis.org/A092553https://oeis.org/A092553https://oeis.org/A092553https://oeis.org/A019774https://oeis.org/A019774https://oeis.org/A019774https://oeis.org/A092605https://oeis.org/A092605https://oeis.org/A092605http://oeis.org/A049470http://oeis.org/A049470http://oeis.org/A049470http://oeis.org/A049469http://oeis.org/A049469http://oeis.org/A049469http://oeis.org/A073226http://oeis.org/A073226http://oeis.org/A073226http://oeis.org/A073230http://oeis.org/A073230http://oeis.org/A073230http://oeis.org/A085660http://oeis.org/A085660http://oeis.org/A085660http://oeis.org/A085659http://oeis.org/A085659http://oeis.org/A085659http://oeis.org/A211883http://oeis.org/A211883http://oeis.org/A211883http://oeis.org/A211884http://oeis.org/A211884http://oeis.org/A211884http://oeis.org/A073229http://oeis.org/A073229http://oeis.org/A073229http://oeis.org/A072364http://oeis.org/A072364http://oeis.org/A072364http://oeis.org/A212436http://oeis.org/A212436http://oeis.org/A212436http://oeis.org/A212437http://oeis.org/A212437http://oeis.org/A212437http://oeis.org/A030178http://oeis.org/A030178http://oeis.org/A030178http://oeis.org/A060295http://oeis.org/A060295http://oeis.org/A060295http://oeis.org/A060295http://oeis.org/A060295http://oeis.org/A019692http://oeis.org/A019692http://oeis.org/A019692http://oeis.org/A049541http://oeis.org/A049541http://oeis.org/A049541http://oeis.org/A002388http://oeis.org/A002388http://oeis.org/A002388http://oeis.org/A092742http://oeis.org/A092742http://oeis.org/A092742http://oeis.org/A002161http://oeis.org/A002161http://oeis.org/A002161http://oeis.org/A087197http://oeis.org/A087197http://oeis.org/A087197http://oeis.org/A053510http://oeis.org/A053510http://oeis.org/A053510http://oeis.org/A053511http://oeis.org/A053511http://oeis.org/A053511http://oeis.org/A231736http://oeis.org/A231736http://oeis.org/A231736http://oeis.org/A231737http://oeis.org/A231737http://oeis.org/A231737http://oeis.org/A073233http://oeis.org/A073233http://oeis.org/A073233http://oeis.org/A073239http://oeis.org/A073239http://oeis.org/A073239http://oeis.org/A073238http://oeis.org/A073238http://oeis.org/A073238http://oeis.org/A073240http://oeis.org/A073240http://oeis.org/A073240http://oeis.org/A222130http://oeis.org/A222130http://oeis.org/A222130http://oeis.org/A222131http://oeis.org/A222131http://oeis.org/A222131http://oeis.org/A222128http://oeis.org/A222128http://oeis.org/A222128http://oeis.org/A222129http://oeis.org/A222129http://oeis.org/A222129http://oeis.org/A236098http://oeis.org/A236098http://oeis.org/A236098http://oeis.org/A236099http://oeis.org/A236099http://oeis.org/A236099http://oeis.org/A236100http://oeis.org/A236100http://oeis.org/A236100http://oeis.org/A236101http://oeis.org/A236101http://oeis.org/A236101http://oeis.org/A236101http://oeis.org/A236100http://oeis.org/A236099http://oeis.org/A236098http://oeis.org/A222129http://oeis.org/A222128http://oeis.org/A222131http://oeis.org/A222130http://oeis.org/A073240http://oeis.org/A073238http://oeis.org/A073239http://oeis.org/A073233http://oeis.org/A231737http://oeis.org/A231736http://oeis.org/A053511http://oeis.org/A053510http://oeis.org/A087197http://oeis.org/A002161http://oeis.org/A092742http://oeis.org/A002388http://oeis.org/A049541http://oeis.org/A019692http://oeis.org/A060295http://oeis.org/A060295http://oeis.org/A030178http://oeis.org/A212437http://oeis.org/A212436http://oeis.org/A072364http://oeis.org/A073229http://oeis.org/A211884http://oeis.org/A211883http://oeis.org/A085659http://oeis.org/A085660http://oeis.org/A073230http://oeis.org/A073226http://oeis.org/A049469http://oeis.org/A049470https://oeis.org/A092605https://oeis.org/A019774https://oeis.org/A092553https://oeis.org/A072334https://oeis.org/A073742https://oeis.org/A073743https://oeis.org/A068985https://oeis.org/A019762


4/25

e 8.539 734 222 673 567 065 463 550 (e) = 2.922 282 365 322 277 864 541 623

e/ 0.865 255 979 432 265 087 217 774 /e= 1.155 727 349 790 921 717 910 093

e= (-1)-i,Gelfond's constant 23.140 692 632 779 269 005 729 086 e-= 0.043 213 918 263 772 249 774 417

e 22.459 157 718 361 045 473 427 152 -e= 0.044 525 267 266 922 906 151 352

e1/ 1.374 802 227 439 358 631 782 821 e-1/= 0.727 377 349 295 216 469 724 148 ...

1/e 1.523 671 054 858 931 718 386 285 -1/e= 0.656 309 639 020 204 707 493 834

sinh()/= (e-e-)/2 3.676 077 910 374 977 720 695 697 Product[n=1..]{1+1/n2)}

Infinite power tower of e/ 0.880 367 778 981 734 621 826 749 also solution of x = (e/)x

Infinite power tower of /e 1.187 523 635 359 249 905 438 407 also solution of x = (/e)x

ei/= cos(1/) i.sin(1/) 0.949 765 715 381 638 659 994 406 i0.312 961 796 207 786 590 745 276

spin-off s and some combinati ons(for basic definition of , see the Basic Constants section)

2 1.154 431 329 803 065 721 213 024 ... 1/ = 1.732 454 714 600 633 473 583 025

ln() -0.549 539 312 981 644 822 337 661 log10() = -2.386 618 912 168 323 894 602 884 ...

e 1.569 034 853 003 742 285 079 907 ... = 1.813 376 492 391 603 499 613 134

e 1.781 072 417 990 197 985 236 504 e-= 0.561 459 483 566 885 169 824 143

Infinite power tower of 0.685 947 035 167 428 481 875 735 ^^^...; also solution of x = x

ei= cos() i sin() 0.837 985 287 880 196 539 954 992 i0.545 692 823 203 992 788 157 356

Golden ratio spin-of fs and combination s(for basic definition of and its inverse , see the Basic Constants section)

Complex golden ratioc= 2.ei/5 1.618 033 988 749 894 848 204 586 +i1.175 570 504 584 946 258 337 411

Associateof = imaginary part of c 1.175 570 504 584 946 258 337 411 2.sin(/5), while = 2.cos(/5) = real part of c

Square root of

1.272 019 649 514 068 964 252 422

; relates the sides of squares withgolden-ratio areas.

Square root of the inverse 0.786 151 377 757 423 286 069 559 1/

Cubic root of 1.173 984 996 705 328 509 966 683 1/3. Relates edges of cubes with golden-ratio volumes.

Cubic root of the inverse 0.851 799 642 079 242 917 055 213 ... 1/1/3

/ = . 1.941 611 038 725 466 577 346 865 Area of golden ellipsewith semi_axes {1,}
https://oeis.org/A019609https://oeis.org/A019609https://oeis.org/A019609https://oeis.org/A019645https://oeis.org/A019645https://oeis.org/A019645https://oeis.org/A061360https://oeis.org/A061360https://oeis.org/A061360https://oeis.org/A061382https://oeis.org/A061382https://oeis.org/A061382http://en.wikipedia.org/wiki/Gelfond%27s_constanthttp://en.wikipedia.org/wiki/Gelfond%27s_constanthttp://en.wikipedia.org/wiki/Gelfond%27s_constanthttps://oeis.org/A039661https://oeis.org/A039661https://oeis.org/A039661https://oeis.org/A093580https://oeis.org/A093580https://oeis.org/A093580https://oeis.org/A059850https://oeis.org/A059850https://oeis.org/A059850https://oeis.org/A092171https://oeis.org/A092171https://oeis.org/A092171https://oeis.org/A179706https://oeis.org/A179706https://oeis.org/A179706https://oeis.org/A205294https://oeis.org/A205294https://oeis.org/A205294https://oeis.org/A231738https://oeis.org/A231738https://oeis.org/A231738https://oeis.org/A156648https://oeis.org/A156648https://oeis.org/A156648http://oeis.org/A231097http://oeis.org/A231097http://oeis.org/A231097http://oeis.org/A231098http://oeis.org/A231098http://oeis.org/A231098http://oeis.org/A237185http://oeis.org/A237185http://oeis.org/A237185http://oeis.org/A237186http://oeis.org/A237186http://oeis.org/A237186https://oeis.org/A098907https://oeis.org/A098907https://oeis.org/A098907https://oeis.org/A002389https://oeis.org/A002389https://oeis.org/A002389http://oeis.org/A203817http://oeis.org/A203817http://oeis.org/A203817https://oeis.org/A073004https://oeis.org/A073004https://oeis.org/A073004https://oeis.org/A080130https://oeis.org/A080130https://oeis.org/A080130http://oeis.org/A231095http://oeis.org/A231095http://oeis.org/A231095https://oeis.org/A119806https://oeis.org/A119806https://oeis.org/A119806https://oeis.org/A119807https://oeis.org/A119807https://oeis.org/A119807https://oeis.org/A001622https://oeis.org/A001622https://oeis.org/A001622https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A139339https://oeis.org/A139339https://oeis.org/A139339https://oeis.org/A197762https://oeis.org/A197762https://oeis.org/A197762https://oeis.org/A139340https://oeis.org/A139340https://oeis.org/A139340https://oeis.org/A094881https://oeis.org/A094881https://oeis.org/A094881https://oeis.org/A094881https://oeis.org/A139340https://oeis.org/A197762https://oeis.org/A139339https://oeis.org/A182007https://oeis.org/A182007https://oeis.org/A001622https://oeis.org/A119807https://oeis.org/A119806http://oeis.org/A231095https://oeis.org/A080130https://oeis.org/A073004http://oeis.org/A203817https://oeis.org/A002389https://oeis.org/A098907http://oeis.org/A237186http://oeis.org/A237185http://oeis.org/A231098http://oeis.org/A231097https://oeis.org/A156648https://oeis.org/A231738https://oeis.org/A205294https://oeis.org/A179706https://oeis.org/A092171https://oeis.org/A059850https://oeis.org/A093580https://oeis.org/A039661http://en.wikipedia.org/wiki/Gelfond%27s_constanthttps://oeis.org/A061382https://oeis.org/A061360https://oeis.org/A019645https://oeis.org/A019609


5/25

ln() = - ln() 0.481 211 825 059 603 447 497 758 Natural logarithm of

2/, such as ingolden spiral 1.358 456 274 182 988 435 206 180 (2/)ln() = 0.306 348 962 530 033 122 115 675

Infinite power tower of the inverse 0.710 439 287 156 503 188 669 345 ^^^...; also solution of x = x= -x

Miscellaneous derived constants:

2^2, theGelfond - Schneider constant 2.665 144 142 690 225 188 650 297 a transcendental number ...

2^2 = 2^(1/2) 1.632 526 919 438 152 844 773 495 ... and its root, also transcendental

Infinite power tower of 1/2 0.641 185 744 504 985 984 486 200 (1/2)^(1/2)^(1^2)^...; also solution of x = 2 -x

Classical, named math constants

Apry's constant(3) 1.202 056 903 159 594 285 399 738 A special value of the Riemann function (x)

Artin's constant 0.373 955 813 619 202 288 054 728 Product[prime p]{1-1/(p(p-1))}

Bernstein's constant 0.280 169 499 023 869 133 036 436 From the theory of function approximations by polynomials

Blazys constant 2.566 543 832 171 388 844 467 529 ItsBlazys' expansiongenerates prime numbers

Brun's constantfor twin primesB4 1.902 160 583 104(?) Sum of reciprocals of prime pairs (p,p+2)

Brun's constantfor prime cousinsB4 1.197 044 9(?) Sum of reciprocals of prime pairs (p,p+4)

Brun's constantfor prime quadruplesB'4 0.870 588 380(?) Sum of reciprocals of prime quadruplets (p,p+2,p+4,p+6)

Cahen's constantC 0.643 410 546 288 338 026 182 254 Alternating-signs sum of Sylvester's sequencereciprocals

Catalan's constantC 0.915 965 594 177 219 015 054 603 C = Sum[n=0,]{(-1)^n/(2n+1)^2}

Champernowne constantC10 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 String concatenation of dec expansions of natural numbers

Continued fractions constant 1.030 640 834 100 712 935 881 776 (1/6)2/(ln(2)ln(10)). Mean c.f.terms per decimal digit

Conway's constant(3) 1.303 577 269 034 296 391 257 099 Growth rate of derived look-and-say strings

Delian's constant 1.259 921 049 894 873 164 767 210 21/3

Embree - Trefethen constant 0.70258(?) Theory of 2nd order recurrences with random add/subtract

Erds - Borwein constant 1.606 695 152 415 291 763 783 301 Sum[n=1,]{1/(2^n -1)}

Feigenbaumreduction parameter -2.502 907 875 095 892 822 283 902 Appears in the theory of chaos
https://oeis.org/A002390https://oeis.org/A002390https://oeis.org/A002390http://en.wikipedia.org/wiki/Golden_spiralhttp://en.wikipedia.org/wiki/Golden_spiralhttp://en.wikipedia.org/wiki/Golden_spiralhttps://oeis.org/A212224https://oeis.org/A212224https://oeis.org/A212224https://oeis.org/A212225https://oeis.org/A212225https://oeis.org/A212225http://oeis.org/A231096http://oeis.org/A231096http://oeis.org/A231096http://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttp://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttp://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttps://oeis.org/A007507https://oeis.org/A007507https://oeis.org/A007507https://oeis.org/A078333https://oeis.org/A078333https://oeis.org/A078333https://oeis.org/A104748https://oeis.org/A104748https://oeis.org/A104748http://en.wikipedia.org/wiki/Ap%C3%A9ry's_constanthttp://en.wikipedia.org/wiki/Ap%C3%A9ry's_constanthttps://oeis.org/A002117https://oeis.org/A002117https://oeis.org/A002117http://en.wikipedia.org/wiki/Artin%27s_constanthttp://en.wikipedia.org/wiki/Artin%27s_constanthttps://oeis.org/A005596https://oeis.org/A005596https://oeis.org/A005596http://en.wikipedia.org/wiki/Bernstein%27s_constanthttp://en.wikipedia.org/wiki/Bernstein%27s_constanthttp://oeis.org/A073001http://oeis.org/A073001http://oeis.org/A073001http://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttp://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttp://oeis.org/A233588http://oeis.org/A233588http://oeis.org/A233588http://en.wikipedia.org/wiki/Brun's_theoremhttp://en.wikipedia.org/wiki/Brun's_theoremhttps://oeis.org/A065421https://oeis.org/A065421https://oeis.org/A065421http://en.wikipedia.org/wiki/Cousin_primehttp://en.wikipedia.org/wiki/Cousin_primehttps://oeis.org/A194098https://oeis.org/A194098https://oeis.org/A194098http://en.wikipedia.org/wiki/Brun's_theoremhttp://en.wikipedia.org/wiki/Brun's_theoremhttps://oeis.org/A213007https://oeis.org/A213007https://oeis.org/A213007http://en.wikipedia.org/wiki/Cahen%27s_constanthttp://en.wikipedia.org/wiki/Cahen%27s_constanthttps://oeis.org/A118227https://oeis.org/A118227https://oeis.org/A118227http://en.wikipedia.org/wiki/Catalan%27s_constanthttp://en.wikipedia.org/wiki/Catalan%27s_constanthttps://oeis.org/A006752https://oeis.org/A006752https://oeis.org/A006752http://en.wikipedia.org/wiki/Champernowne_constanthttp://en.wikipedia.org/wiki/Champernowne_constanthttps://oeis.org/A033307https://oeis.org/A033307https://oeis.org/A033307http://mathworld.wolfram.com/LochsTheorem.htmlhttp://mathworld.wolfram.com/LochsTheorem.htmlhttps://oeis.org/A062542https://oeis.org/A062542https://oeis.org/A062542http://en.wikipedia.org/wiki/Conway%27s_constanthttp://en.wikipedia.org/wiki/Conway%27s_constanthttp://oeis.org/A014715http://oeis.org/A014715http://oeis.org/A014715http://mathworld.wolfram.com/DelianConstant.htmlhttp://mathworld.wolfram.com/DelianConstant.htmlhttp://oeis.org/A002580http://oeis.org/A002580http://oeis.org/A002580http://en.wikipedia.org/wiki/Embree%E2%80%93Trefethen_constanthttp://en.wikipedia.org/wiki/Embree%E2%80%93Trefethen_constanthttp://oeis.org/A118288http://oeis.org/A118288http://oeis.org/A118288http://mathworld.wolfram.com/Erdos-BorweinConstant.htmlhttp://mathworld.wolfram.com/Erdos-BorweinConstant.htmlhttp://oeis.org/A065442http://oeis.org/A065442http://oeis.org/A065442http://mathworld.wolfram.com/FeigenbaumConstant.htmlhttp://mathworld.wolfram.com/FeigenbaumConstant.htmlhttp://oeis.org/A006891http://oeis.org/A006891http://oeis.org/A006891http://oeis.org/A006891http://mathworld.wolfram.com/FeigenbaumConstant.htmlhttp://oeis.org/A065442http://mathworld.wolfram.com/Erdos-BorweinConstant.htmlhttp://oeis.org/A118288http://en.wikipedia.org/wiki/Embree%E2%80%93Trefethen_constanthttp://oeis.org/A002580http://mathworld.wolfram.com/DelianConstant.htmlhttp://oeis.org/A014715http://en.wikipedia.org/wiki/Conway%27s_constanthttps://oeis.org/A062542http://mathworld.wolfram.com/LochsTheorem.htmlhttps://oeis.org/A033307http://en.wikipedia.org/wiki/Champernowne_constanthttps://oeis.org/A006752http://en.wikipedia.org/wiki/Catalan%27s_constanthttps://oeis.org/A118227http://en.wikipedia.org/wiki/Cahen%27s_constanthttps://oeis.org/A213007http://en.wikipedia.org/wiki/Brun's_theoremhttps://oeis.org/A194098http://en.wikipedia.org/wiki/Cousin_primehttps://oeis.org/A065421http://en.wikipedia.org/wiki/Brun's_theoremhttp://oeis.org/A233588http://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttp://oeis.org/A073001http://en.wikipedia.org/wiki/Bernstein%27s_constanthttps://oeis.org/A005596http://en.wikipedia.org/wiki/Artin%27s_constanthttps://oeis.org/A002117http://en.wikipedia.org/wiki/Ap%C3%A9ry's_constanthttps://oeis.org/A104748https://oeis.org/A078333https://oeis.org/A007507http://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttp://oeis.org/A231096https://oeis.org/A212225https://oeis.org/A212224http://en.wikipedia.org/wiki/Golden_spiralhttps://oeis.org/A002390


6/25

Feigenbaumbifurcation velocity 4.669 201 609 102 990 671 853 203 Appears in the theory of chaos

Fransn-Robinson constant 2.807 770 242 028 519 365 221 501 Integral[[x=0..]{1/(x)}; see Gamma function

Gauss' constantG 0.834 626 841 674 073 186 814 297 1/agm(1,2); agm ... arithmetic-geometric mean

Gauss-Kuzmin-Wirsing constant1 0.303 663 002 898 732 658 597 448 2nd eigenvalue of GKW functional operator (first is 1)

Gelfond's constant 23.140 692 632 779 269 005 729 086 e^ = (-1)^(-i)

Gelfond - Schneider constant 2.665 144 142 690 225 188 650 297 2^2, a transcendental number

Gerver's moving sofa constant 2.219 531 668 871 97 (? largest so far) A sofa that can turn unit-width hallway corner

Hammersley'supper bound on Gerver's constant 2.207 416 099 162 477 962 306 856 /2 + 2/. Also themean angle of a random rotation.

Gibbs constantG 1.851 937 051 982 466 170 361 053 Si(), Integral[x=0..pi;]{sin(x)/x}.

Wilbraham-Gibbs constantG' 1.178 979 744 472 167 270 232 028 (2/)*(Gibbs constant G).

Glaisher-Kinkelin constantA 1.282 427 129 100 622 636 875 342 Appears in number theory

Golomb-Dickman constant 0.624 329 988 543 550 870 992 936 Longest cycle distribution in random permutations

Gompertz constantG 0.596 347 362 323 194 074 341 078 -e.Ei(-1), Ei(x) being the exponential integral

Grossmann's constant 0.737 338 303 369 29(?) The only x for which {a0=1; a1=x; an+2=an/(1+an+1)} converges

Khinchin's constantK, K0 2.685 452 001 065 306 445 309 714 Limit geom.mean of continued fractions quotients (most reals)

Khinchin-Lvy constant 3.275 822 918 721 811 159 787 681 exp(2/(12.ln2)); unstable nomenclature

Knuth's random-generators constant 0.211 324 865 405 187 117 745 425 (1-(1/3))/2

Kolakoski constant 0.794 507 192 779 479 276 240 362 Related to Kolakoski sequence

Landau-Ramanujan constant 0.764 223 653 589 220 662 990 698 Related to the density of sums of two integer squares

Laplace limit constant 0.662 743 419 349 181 580 974 742 Let = (1+2); then e= 1+Click here for more

Lemniscate constantL

2.622 057 554 292 119 810 464 839

L = G, where G is the Gauss' constant

First lemniscate constantLA 1.311 028 777 146 059 905 232 419 LA= L/2 = G/2

Second lemniscate constantLB 0.599 070 117 367 796 103 337 484 LB= 1/(2G)

Lvy constant 1.186 569 110 415 625 452 821 722 2/(12.ln2). Logarithm of Khinchin-Lvy's

Liouville's constant 0.110 001 000 000 000 000 000 001 Sum[n=0,]{10^(-n!)}
http://mathworld.wolfram.com/FeigenbaumConstant.htmlhttp://mathworld.wolfram.com/FeigenbaumConstant.htmlhttp://oeis.org/A006890http://oeis.org/A006890http://oeis.org/A006890http://mathworld.wolfram.com/Fransen-RobinsonConstant.htmlhttp://mathworld.wolfram.com/Fransen-RobinsonConstant.htmlhttps://oeis.org/A058655https://oeis.org/A058655https://oeis.org/A058655http://en.wikipedia.org/wiki/Gauss's_constanthttp://en.wikipedia.org/wiki/Gauss's_constanthttps://oeis.org/A014549https://oeis.org/A014549https://oeis.org/A014549http://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing_constanthttp://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing_constanthttp://oeis.org/A038517http://oeis.org/A038517http://oeis.org/A038517http://en.wikipedia.org/wiki/Gelfond%27s_constanthttp://en.wikipedia.org/wiki/Gelfond%27s_constanthttps://oeis.org/A039661https://oeis.org/A039661https://oeis.org/A039661http://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttp://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttps://oeis.org/A007507https://oeis.org/A007507https://oeis.org/A007507http://en.wikipedia.org/wiki/Moving_sofa_problemhttp://en.wikipedia.org/wiki/Moving_sofa_problemhttps://oeis.org/A086118https://oeis.org/A086118https://oeis.org/A086118http://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttp://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttps://oeis.org/A036792https://oeis.org/A036792https://oeis.org/A036792http://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttp://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttps://oeis.org/A036793https://oeis.org/A036793https://oeis.org/A036793http://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constanthttp://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constanthttps://oeis.org/A074962https://oeis.org/A074962https://oeis.org/A074962http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constanthttp://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constanthttps://oeis.org/A084945https://oeis.org/A084945https://oeis.org/A084945http://mathworld.wolfram.com/GompertzConstant.htmlhttp://mathworld.wolfram.com/GompertzConstant.htmlhttps://oeis.org/A073003https://oeis.org/A073003https://oeis.org/A073003http://mathworld.wolfram.com/GrossmansConstant.htmlhttp://mathworld.wolfram.com/GrossmansConstant.htmlhttps://oeis.org/A085835https://oeis.org/A085835https://oeis.org/A085835http://mathworld.wolfram.com/KhinchinsConstanthttp://mathworld.wolfram.com/KhinchinsConstanthttps://oeis.org/A002210https://oeis.org/A002210https://oeis.org/A002210http://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttp://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttps://oeis.org/A086702https://oeis.org/A086702https://oeis.org/A086702http://www.ebyte.it/library/educards/constants/MathConstants.html#knuthhttp://www.ebyte.it/library/educards/constants/MathConstants.html#knuthhttps://oeis.org/A156309https://oeis.org/A156309https://oeis.org/A156309http://mathworld.wolfram.com/KolakoskiSequence.htmlhttp://mathworld.wolfram.com/KolakoskiSequence.htmlhttps://oeis.org/A118270https://oeis.org/A118270https://oeis.org/A118270http://mathworld.wolfram.com/Landau-RamanujanConstant.htmlhttp://mathworld.wolfram.com/Landau-RamanujanConstant.htmlhttps://oeis.org/A064533https://oeis.org/A064533https://oeis.org/A064533http://en.wikipedia.org/wiki/Laplace_limithttp://en.wikipedia.org/wiki/Laplace_limithttps://oeis.org/A033259https://oeis.org/A033259https://oeis.org/A033259http://mathworld.wolfram.com/LaplaceLimit.htmlhttp://mathworld.wolfram.com/LaplaceLimit.htmlhttp://mathworld.wolfram.com/LaplaceLimit.htmlhttp://mathworld.wolfram.com/LemniscateConstant.htmlhttp://mathworld.wolfram.com/LemniscateConstant.htmlhttps://oeis.org/A062539https://oeis.org/A062539https://oeis.org/A062539http://mathworld.wolfram.com/LemniscateConstant.htmlhttp://mathworld.wolfram.com/LemniscateConstant.htmlhttps://oeis.org/A085565https://oeis.org/A085565https://oeis.org/A085565http://mathworld.wolfram.com/LemniscateConstant.htmlhttp://mathworld.wolfram.com/LemniscateConstant.htmlhttps://oeis.org/A076390https://oeis.org/A076390https://oeis.org/A076390http://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttp://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttps://oeis.org/A100199https://oeis.org/A100199https://oeis.org/A100199http://en.wikipedia.org/wiki/Liouville%27s_constanthttp://en.wikipedia.org/wiki/Liouville%27s_constanthttps://oeis.org/A012245https://oeis.org/A012245https://oeis.org/A012245https://oeis.org/A012245http://en.wikipedia.org/wiki/Liouville%27s_constanthttps://oeis.org/A100199http://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttps://oeis.org/A076390http://mathworld.wolfram.com/LemniscateConstant.htmlhttps://oeis.org/A085565http://mathworld.wolfram.com/LemniscateConstant.htmlhttps://oeis.org/A062539http://mathworld.wolfram.com/LemniscateConstant.htmlhttp://mathworld.wolfram.com/LaplaceLimit.htmlhttps://oeis.org/A033259http://en.wikipedia.org/wiki/Laplace_limithttps://oeis.org/A064533http://mathworld.wolfram.com/Landau-RamanujanConstant.htmlhttps://oeis.org/A118270http://mathworld.wolfram.com/KolakoskiSequence.htmlhttps://oeis.org/A156309http://www.ebyte.it/library/educards/constants/MathConstants.html#knuthhttps://oeis.org/A086702http://en.wikipedia.org/wiki/Khinchin%E2%80%93L%C3%A9vy_constanthttps://oeis.org/A002210http://mathworld.wolfram.com/KhinchinsConstanthttps://oeis.org/A085835http://mathworld.wolfram.com/GrossmansConstant.htmlhttps://oeis.org/A073003http://mathworld.wolfram.com/GompertzConstant.htmlhttps://oeis.org/A084945http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constanthttps://oeis.org/A074962http://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constanthttps://oeis.org/A036793http://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttps://oeis.org/A036792http://mathworld.wolfram.com/Wilbraham-GibbsConstant.htmlhttps://oeis.org/A086118http://en.wikipedia.org/wiki/Moving_sofa_problemhttps://oeis.org/A007507http://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constanthttps://oeis.org/A039661http://en.wikipedia.org/wiki/Gelfond%27s_constanthttp://oeis.org/A038517http://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing_constanthttps://oeis.org/A014549http://en.wikipedia.org/wiki/Gauss's_constanthttps://oeis.org/A058655http://mathworld.wolfram.com/Fransen-RobinsonConstant.htmlhttp://oeis.org/A006890http://mathworld.wolfram.com/FeigenbaumConstant.html


7/25

Loch's constant 0.970 270 114 392 033 925 740 256 6.ln(2).ln(10)/2; convergence rate of continued fractions

Madelung's constantM3 -1.747 564 594 633 182 190 636 212 M3= Sum[i,j,k]{(-1)^(i+j+k)/sqr(i^2+j^2+k^2)}

Meissel-Mertens constantB1 0.261 497 212 847 642 783 755 426 Limit[n]{Sum[prime pn]{1/p}-ln(ln(n))}

MRB constant 0.187 859 642 462 067 120 248 517 Sum[n=1,2,...]{(-1)^n (n^(1/n) - 1)}

MKB constant 0.687 652 368 927 694 369 809 3 Limit[n]{abs(Integral[x=1..2n]{(-1)^x x^(1/x)}}

Omega constantW(1) 0.567 143 290 409 783 872 999 968 Root of [x - e-x] or [x + ln(x)].See also.

Otter's constant 2.955 765 285 651 994 974 714 817 Appears in enumeration of rooted and unrooted trees:

Otter's asymptotic constantufor unrooted trees 0.534 949 606 1(?) UT(n) ~ u n n-5/2

Otter's asymptotic constantrfor rooted trees 0.439 924 012 571 (?) RT(n) ~ r n n-3/2(V. Kotesovec)

Plastic number (orsilver constant) 1.324 717 957 244 746 025 960 908 Real root of x3= x + 1

Pogson's ratio 2.511 886 431 509 580 111 085 032 1001/5; in astronomy 1 stellar magnitude brightness ratio

Polya's random-walk constantp3 0.340 537 329 550 999 142 826 273 Probability a 3D-lattice random walk returns back.See also

Prvost's constant(Reciprocal Fibonacci) 3.359 885 666 243 177 553 172 011 Sum of reciprocals of Fibonacci numbers

Reciprocal even Fibonacci constant 1.535 370 508 836 252 985 029 852 Sum of reciprocals of even-indexed Fibonacci numbers

Reciprocal odd Fibonacci constant 1.824 515 157 406 924 568 142 158 Sum of reciprocals of odd-indexed Fibonacci numbers

Rnyi's parking constantm 0.747 597 920 253 411 435 178 730 Density of randomly parked cars in a street

Salem number1 1.176 280 818 259 917 506 544 070 Related to the structure of the set of algebraic integers

Sierpinski's constantK 2.584 981 759 579 253 217 065 893 For explanation,click also here

Soldner's constant 1.451 369 234 883 381 050 283 968 Root oflogarithmic integralli(x)

Somos' quadratic recurrence constant 1.661 687 949 633 594 121 295 818 (1(2(3(4 ...))))

Shall-Wilsonortwin primesconstant C2

0.660 161 815 846 869 573 927 812

Product[twin_primes p,p+2]{p(p-2)/(p-1)

2

}

Theodorus' constant 1.732 050 807 568 877 293 527 446 3.

Viswanath's constant 1.131 988 248 794 3(?) Growth of Fibonacci-like sequences with random add/subtract

Some other, notable math constants
http://mathworld.wolfram.com/LochsTheoremhttp://mathworld.wolfram.com/LochsTheoremhttps://oeis.org/A086819https://oeis.org/A086819https://oeis.org/A086819http://en.wikipedia.org/wiki/Madelung_constanthttp://en.wikipedia.org/wiki/Madelung_constanthttps://oeis.org/A085469https://oeis.org/A085469https://oeis.org/A085469http://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constanthttp://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constanthttps://oeis.org/A077761https://oeis.org/A077761https://oeis.org/A077761http://marvinrayburns.com/new_on_mrb.htmlhttp://marvinrayburns.com/new_on_mrb.htmlhttps://oeis.org/A037077https://oeis.org/A037077https://oeis.org/A037077http://marvinrayburns.com/new_on_mrb.htmlhttp://marvinrayburns.com/new_on_mrb.htmlhttps://oeis.org/A157852https://oeis.org/A157852https://oeis.org/A157852http://mathworld.wolfram.com/OmegaConstant.htmlhttp://mathworld.wolfram.com/OmegaConstant.htmlhttps://oeis.org/A030178https://oeis.org/A030178https://oeis.org/A030178http://en.wikipedia.org/wiki/Omega_constanthttp://en.wikipedia.org/wiki/Omega_constanthttp://en.wikipedia.org/wiki/Omega_constanthttp://mathworld.wolfram.com/Tree.htmlhttp://mathworld.wolfram.com/Tree.htmlhttps://oeis.org/A051491https://oeis.org/A051491https://oeis.org/A051491http://mathworld.wolfram.com/Tree.htmlhttp://mathworld.wolfram.com/Tree.htmlhttps://oeis.org/A086308https://oeis.org/A086308https://oeis.org/A086308https://oeis.org/A187770https://oeis.org/A187770https://oeis.org/A187770http://en.wikipedia.org/wiki/Plastic_numberhttp://en.wikipedia.org/wiki/Plastic_numberhttps://oeis.org/A060006https://oeis.org/A060006https://oeis.org/A060006http://en.wikipedia.org/wiki/Norman_Robert_Pogsonhttp://en.wikipedia.org/wiki/Norman_Robert_Pogsonhttps://oeis.org/A189824https://oeis.org/A189824https://oeis.org/A189824http://mathworld.wolfram.com/PolyasRandomWalkConstants.htmlhttp://mathworld.wolfram.com/PolyasRandomWalkConstants.htmlhttps://oeis.org/A086230https://oeis.org/A086230https://oeis.org/A086230http://en.wikipedia.org/wiki/Random_walkhttp://en.wikipedia.org/wiki/Random_walkhttp://en.wikipedia.org/wiki/Random_walkhttp://www.numericana.com/data/prevost.htmhttp://www.numericana.com/data/prevost.htmhttp://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constanthttp://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constanthttp://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constanthttps://oeis.org/A079586https://oeis.org/A079586https://oeis.org/A079586http://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttp://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttps://oeis.org/A153386https://oeis.org/A153386https://oeis.org/A153386http://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttp://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttps://oeis.org/A153387https://oeis.org/A153387https://oeis.org/A153387http://mathworld.wolfram.com/RenyisParkingConstants.htmlhttp://mathworld.wolfram.com/RenyisParkingConstants.htmlhttps://oeis.org/A050996https://oeis.org/A050996https://oeis.org/A050996http://mathworld.wolfram.com/SalemConstants.htmlhttp://mathworld.wolfram.com/SalemConstants.htmlhttps://oeis.org/A073011https://oeis.org/A073011https://oeis.org/A073011http://en.wikipedia.org/wiki/Sierpi%C5%84ski%27s_constanthttp://en.wikipedia.org/wiki/Sierpi%C5%84ski%27s_constanthttps://oeis.org/A062089https://oeis.org/A062089https://oeis.org/A062089http://mathworld.wolfram.com/SierpinskiConstant.htmlhttp://mathworld.wolfram.com/SierpinskiConstant.htmlhttp://mathworld.wolfram.com/SierpinskiConstant.htmlhttp://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constanthttp://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constanthttps://oeis.org/A070769https://oeis.org/A070769https://oeis.org/A070769http://mathworld.wolfram.com/LogarithmicIntegral.htmlhttp://mathworld.wolfram.com/LogarithmicIntegral.htmlhttp://mathworld.wolfram.com/LogarithmicIntegral.htmlhttp://en.wikipedia.org/wiki/Somos'_quadratic_recurrence_constanthttp://en.wikipedia.org/wiki/Somos'_quadratic_recurrence_constanthttps://oeis.org/A112302https://oeis.org/A112302https://oeis.org/A112302http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.htmlhttp://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.htmlhttp://en.wikipedia.org/wiki/Twin_prime_constanthttp://en.wikipedia.org/wiki/Twin_prime_constanthttp://en.wikipedia.org/wiki/Twin_prime_constanthttps://oeis.org/A005597https://oeis.org/A005597https://oeis.org/A005597http://mathworld.wolfram.com/TheodorussConstant.htmlhttp://mathworld.wolfram.com/TheodorussConstant.htmlhttps://oeis.org/A002194https://oeis.org/A002194https://oeis.org/A002194http://en.wikipedia.org/wiki/Random_Fibonacci_sequencehttp://en.wikipedia.org/wiki/Random_Fibonacci_sequencehttps://oeis.org/A078416https://oeis.org/A078416https://oeis.org/A078416https://oeis.org/A078416http://en.wikipedia.org/wiki/Random_Fibonacci_sequencehttps://oeis.org/A002194http://mathworld.wolfram.com/TheodorussConstant.htmlhttps://oeis.org/A005597http://en.wikipedia.org/wiki/Twin_prime_constanthttp://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.htmlhttps://oeis.org/A112302http://en.wikipedia.org/wiki/Somos'_quadratic_recurrence_constanthttp://mathworld.wolfram.com/LogarithmicIntegral.htmlhttps://oeis.org/A070769http://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constanthttp://mathworld.wolfram.com/SierpinskiConstant.htmlhttps://oeis.org/A062089http://en.wikipedia.org/wiki/Sierpi%C5%84ski%27s_constanthttps://oeis.org/A073011http://mathworld.wolfram.com/SalemConstants.htmlhttps://oeis.org/A050996http://mathworld.wolfram.com/RenyisParkingConstants.htmlhttps://oeis.org/A153387http://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttps://oeis.org/A153386http://mathworld.wolfram.com/ReciprocalFibonacciConstant.htmlhttps://oeis.org/A079586http://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constanthttp://www.numericana.com/data/prevost.htmhttp://en.wikipedia.org/wiki/Random_walkhttps://oeis.org/A086230http://mathworld.wolfram.com/PolyasRandomWalkConstants.htmlhttps://oeis.org/A189824http://en.wikipedia.org/wiki/Norman_Robert_Pogsonhttps://oeis.org/A060006http://en.wikipedia.org/wiki/Plastic_numberhttps://oeis.org/A187770https://oeis.org/A086308http://mathworld.wolfram.com/Tree.htmlhttps://oeis.org/A051491http://mathworld.wolfram.com/Tree.htmlhttp://en.wikipedia.org/wiki/Omega_constanthttps://oeis.org/A030178http://mathworld.wolfram.com/OmegaConstant.htmlhttps://oeis.org/A157852http://marvinrayburns.com/new_on_mrb.htmlhttps://oeis.org/A037077http://marvinrayburns.com/new_on_mrb.htmlhttps://oeis.org/A077761http://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constanthttps://oeis.org/A085469http://en.wikipedia.org/wiki/Madelung_constanthttps://oeis.org/A086819http://mathworld.wolfram.com/LochsTheorem


8/25

(1-1/2)*(1-1/4)*(1-1/8)*(1-1/16)* ... 0.288 788 095 086 602 421 278 899 Product[k=1..]{1-xk}, for x=1/2

1+1/22+1/33+1/44+ ... 1.291 285 997 062 663 540 407 282 Sum[k=1,] (1/kk)

Alt ernating sums of in verse powers of prime numbers, sip(x) = -Sum[n=1,2,3,...]{(-1)^n/p(n)^x}, where p(n) is the n -th integer

sip(1/2) 0.347 835 4 ... 1/2 -1/3 +1/5 -1/7 +1/11 -1/13 +1/17 -...

sip(1) 0.269 606 351 916 7 1/2 -1/3 +1/5 -1/7 +1/11 -1/13 +1/17 -...

sip(2) 0.162 816 246 663 601 41 1/2^2 -1/3^2 +1/5^2 -1/7^2 +1/11^2 -1/13^2 +...

sip(3) 0.093 463 631 399 649 889 112 4 1/2^3 -1/3^3 +1/5^3 -1/7^3 +1/11^3 -1/13^3 +...

sip(4) 0.051 378 305 166 748 282 575 200 1/2^4 -1/3^4 +1/5^4 -1/7^4 +1/11^4 -1/13^4 +...

sip(5) 0.027 399 222 614 542 740 586 273 1/2^5 -1/3^5 +1/5^5 -1/7^5 +1/11^5 -1/13^5 +...

Values ofspecial continu ed fractionsa1+a1/(a2+a2/(a3+a3/(a4+...))) for some integer sequences a= {a1,a2,a3,a4,...}. See Blazys constantfor primes.

a natural numbers: {1,2,3,4,...} 1.392 211 191 177 332 814 376 552 = 1/(e-2)

a squares: {1,4,9,16,...} 1.226 284 024 182 690 274 814 937

a powers of 2: {1,2,4,8,...} 1.408 615 979 735 005 205 132 362

a factorials: {0!,1!,2!,4!,...} 1.698 804 767 670 007 211 952 690

Selected natural and integer numbers

Lar ge integers

Googol 10100= 10^100 A large integer ...

Googolplex 10googol= 10^10^100 ... a larger integer ...

Googolplexplex 10googolplex= 10^10^10^100 ... and a still larger one.

Graham's number(last 20 digits) ... 04575627262464195387 3^^^...^^^3, with 64 power operators; too big to write

Skewes' numbers 10^14 < n < e^e^e^79 Bounds on the first integer for which (n) < li(n)

Bernay's' number 67^257^729 Originally an example of ahardly ever used number

Vari ous interesting in tegers

Largest integer not composed of two abundants 20161 Exactly 1456 integers are thesum of two abundants
http://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttps://oeis.org/A048651https://oeis.org/A048651https://oeis.org/A048651http://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttp://mrob.com/pub/math/numbers.htmlhttps://oeis.org/A073009https://oeis.org/A073009https://oeis.org/A073009https://oeis.org/A078437https://oeis.org/A078437https://oeis.org/A078437https://oeis.org/A242301https://oeis.org/A242301https://oeis.org/A242301https://oeis.org/A242302https://oeis.org/A242302https://oeis.org/A242302https://oeis.org/A242303https://oeis.org/A242303https://oeis.org/A242303https://oeis.org/A242304https://oeis.org/A242304https://oeis.org/A242304http://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttp://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttp://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttps://oeis.org/A194807https://oeis.org/A194807https://oeis.org/A194807https://oeis.org/A233591https://oeis.org/A233591https://oeis.org/A233591https://oeis.org/A233590https://oeis.org/A233590https://oeis.org/A233590https://oeis.org/A233589https://oeis.org/A233589https://oeis.org/A233589http://en.wikipedia.org/wiki/Googolhttp://en.wikipedia.org/wiki/Googolhttp://en.wikipedia.org/wiki/Googolplexhttp://en.wikipedia.org/wiki/Googolplexhttp://en.wikipedia.org/wiki/Names_of_large_numbers#The_googol_familyhttp://en.wikipedia.org/wiki/Names_of_large_numbers#The_googol_familyhttp://en.wikipedia.org/wiki/Graham's_numberhttp://en.wikipedia.org/wiki/Graham's_numberhttp://en.wikipedia.org/wiki/Skewes%27_numberhttp://en.wikipedia.org/wiki/Skewes%27_numberhttp://oeis.org/A160106http://oeis.org/A160106http://wab.uib.no/ojs/agora-alws/article/view/2743/3210http://wab.uib.no/ojs/agora-alws/article/view/2743/3210http://wab.uib.no/ojs/agora-alws/article/view/2743/3210http://mathworld.wolfram.com/AbundantNumber.htmlhttp://mathworld.wolfram.com/AbundantNumber.htmlhttps://oeis.org/A048242https://oeis.org/A048242https://oeis.org/A048242https://oeis.org/A048242http://mathworld.wolfram.com/AbundantNumber.htmlhttp://wab.uib.no/ojs/agora-alws/article/view/2743/3210http://oeis.org/A160106http://en.wikipedia.org/wiki/Skewes%27_numberhttp://en.wikipedia.org/wiki/Graham's_numberhttp://en.wikipedia.org/wiki/Names_of_large_numbers#The_googol_familyhttp://en.wikipedia.org/wiki/Googolplexhttp://en.wikipedia.org/wiki/Googolhttps://oeis.org/A233589https://oeis.org/A233590https://oeis.org/A233591https://oeis.org/A194807http://www.ebyte.it/library/docs/math13/BlazysExpansions.htmlhttps://oeis.org/A242304https://oeis.org/A242303https://oeis.org/A242302https://oeis.org/A242301https://oeis.org/A078437https://oeis.org/A073009http://mrob.com/pub/math/numbers.htmlhttps://oeis.org/A048651http://mrob.com/pub/math/numbers.html


9/25

Hardy-Ramanujan number 1729 = 13+123= 93+103 Smallest cubefree taxicab numberT(2); see below

Heegner numbersh (full set) 1, 2, 3, 7, 11, 19, 43, 67, 163 The quadratic ring Q((-h)) has class number 1

Vojta's number 15170835645 Smallest cubefree T(3) taxicab number (see the link)

Gascoigne's number 1801049058342701083 Smallest cubefree T(4) taxicab number (see the link)

Ishango bone prime quadruplet 11, 13, 17, 19 Crafted in the paleolithicIshango bone

Largest factorionin base 10 40585 Equals the sum of factorials of its dec digits

Largest factorionin base 16 2615428934649 Equals the sum of factorials of its hex digits

Largest right-truncatable prime in base 10 73939133 (seeA023107) Truncate any digits on the right and it's still a prime.

Largest left-truncatable prime in base 10 357686312646216567629137 Truncate any digits on the left and it's still prime. See A103443.

Largest right-truncatable prime in base 16 hex 3B9BF319BD51FF (seeA237600) Truncate any hex digits on the right and it's still a prime.

Belphegor's PrimeB(13); next one is B(42). 1000000000000066600000000000001 Belphegor is one of the seven princes of Hell. See A232448.

Selected sequences of natural and integer numbers

Polygonal (2D) figurate numbers.See also on OEIS: numbers which are (A090466)or aren't (A090467)"some" polygonal number. See the link for more!

Triangualar numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, n(n+1)/2

Square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81,100,121, n*n

Pentagonal numbers 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, n(3n-1)/2

Hexagonal numbers 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, n(2n-1); also cornered hexagonal numbers

Heptagonal numbers 1, 7, 18, 34, 55, 81, 112, 148, 189, n(5n-3)/2

Octagonal numbers 1, 8, 21, 40, 65, 96, 133, 176, 225, n(3n-2)

Square-triangular numbers 1,36,1225,41616,1413721,48024900, [[(3+22)k-(3-22)k]/(42)]2; both triangular and square

Centered polygonal (2D) fi gurate numbers

Centered triangular numbers 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, (3n2+3n+2)/2. See also: centered triangular primes

Centered square numbers 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 2n2-2n+1. See also: centered square primes

Centered pentagonal numbers 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, (5(n-1)2+5(n-1)+2)/2. See also: centered pentagonal primes
http://theinfosphere.org/1729_(number)http://theinfosphere.org/1729_(number)https://oeis.org/A080642https://oeis.org/A080642http://en.wikipedia.org/wiki/Heegner_numberhttp://en.wikipedia.org/wiki/Heegner_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Prime_quadruplethttp://en.wikipedia.org/wiki/Prime_quadruplethttp://en.wikipedia.org/wiki/Ishango_bonehttp://en.wikipedia.org/wiki/Ishango_bonehttp://en.wikipedia.org/wiki/Ishango_bonehttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://mathworld.wolfram.com/AbundantNumber.htmlhttp://mathworld.wolfram.com/AbundantNumber.htmlhttps://oeis.org/A023107https://oeis.org/A023107https://oeis.org/A023107http://en.wikipedia.org/wiki/Truncatable_prime.htmlhttp://en.wikipedia.org/wiki/Truncatable_prime.htmlhttps://oeis.org/A103443https://oeis.org/A103443https://oeis.org/A103443http://mathworld.wolfram.com/AbundantNumber.htmlhttp://mathworld.wolfram.com/AbundantNumber.htmlhttps://oeis.org/A237600https://oeis.org/A237600https://oeis.org/A237600http://en.wikipedia.org/wiki/Palindromic_prime.htmlhttp://en.wikipedia.org/wiki/Palindromic_prime.htmlhttps://oeis.org/A232448https://oeis.org/A232448https://oeis.org/A232448http://en.wikipedia.org/wiki/Polygonal_numberhttp://en.wikipedia.org/wiki/Polygonal_numberhttps://oeis.org/A090466https://oeis.org/A090466https://oeis.org/A090466https://oeis.org/A090467https://oeis.org/A090467https://oeis.org/A090467http://en.wikipedia.org/wiki/Triangular_numberhttp://en.wikipedia.org/wiki/Triangular_numberhttp://oeis.org/A000217http://oeis.org/A000217http://oeis.org/A000217http://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Square_numberhttp://oeis.org/A000290http://oeis.org/A000290http://oeis.org/A000290http://en.wikipedia.org/wiki/Pentagonal_numberhttp://en.wikipedia.org/wiki/Pentagonal_numberhttp://oeis.org/A000326http://oeis.org/A000326http://oeis.org/A000326http://en.wikipedia.org/wiki/Hexagonal_numberhttp://en.wikipedia.org/wiki/Hexagonal_numberhttp://oeis.org/A000384http://oeis.org/A000384http://oeis.org/A000384http://en.wikipedia.org/wiki/Heptagonal_numberhttp://en.wikipedia.org/wiki/Heptagonal_numberhttp://oeis.org/A000566http://oeis.org/A000566http://oeis.org/A000566http://en.wikipedia.org/wiki/Octagonal_numberhttp://en.wikipedia.org/wiki/Octagonal_numberhttp://oeis.org/A000567http://oeis.org/A000567http://oeis.org/A000567http://en.wikipedia.org/wiki/Square_triangular_numberhttp://en.wikipedia.org/wiki/Square_triangular_numberhttp://oeis.org/A001110http://oeis.org/A001110http://oeis.org/A001110http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A005448http://oeis.org/A005448http://oeis.org/A005448http://oeis.org/A125602http://oeis.org/A125602http://oeis.org/A125602http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A001844http://oeis.org/A001844http://oeis.org/A001844http://oeis.org/A027862http://oeis.org/A027862http://oeis.org/A027862http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A005891http://oeis.org/A005891http://oeis.org/A005891http://oeis.org/A145838http://oeis.org/A145838http://oeis.org/A145838http://oeis.org/A145838http://oeis.org/A005891http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A027862http://oeis.org/A001844http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A125602http://oeis.org/A005448http://en.wikipedia.org/wiki/Centered_triangular_numberhttp://oeis.org/A001110http://en.wikipedia.org/wiki/Square_triangular_numberhttp://oeis.org/A000567http://en.wikipedia.org/wiki/Octagonal_numberhttp://oeis.org/A000566http://en.wikipedia.org/wiki/Heptagonal_numberhttp://oeis.org/A000384http://en.wikipedia.org/wiki/Hexagonal_numberhttp://oeis.org/A000326http://en.wikipedia.org/wiki/Pentagonal_numberhttp://oeis.org/A000290http://en.wikipedia.org/wiki/Square_numberhttp://oeis.org/A000217http://en.wikipedia.org/wiki/Triangular_numberhttps://oeis.org/A090467https://oeis.org/A090466http://en.wikipedia.org/wiki/Polygonal_numberhttps://oeis.org/A232448http://en.wikipedia.org/wiki/Palindromic_prime.htmlhttps://oeis.org/A237600http://mathworld.wolfram.com/AbundantNumber.htmlhttps://oeis.org/A103443http://en.wikipedia.org/wiki/Truncatable_prime.htmlhttps://oeis.org/A023107http://mathworld.wolfram.com/AbundantNumber.htmlhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Ishango_bonehttp://en.wikipedia.org/wiki/Prime_quadruplethttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Heegner_numberhttps://oeis.org/A080642http://theinfosphere.org/1729_(number)


10/25

Centered hexagonal numbers 1, 7, 19, 37, 61, 91, 127, 169, 217, n3- (n-1)3= 3n(n-1)+1; also hex numbers

Centered heptagonal numbers 1, 8, 22, 43, 71, 106, 148, 197, 253, (7n2-7n+2)/2

Centered octagonal numbers 1, 9, 25, 49, 81, 121, 169, 225, 289, (2n-1)2; squares of odd numbers

Polyhedral (3D) figur ate numbers

Tetrahedral numbersTn 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, n(n+1)(n+2)/6. Only three are squares: 1, 4, 19600

Cubic numbers,cubes 1, 8, 27, 64, 125, 216, 343, 512, 729, n3

Pentatopic (or pentachoron) numbers 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, n(n+1)(n+2)(n+3)/24; n=0,1,2,...

Octahedral numbersOn 1, 6, 19, 44, 85, 146, 231, 344, 489, n(2n2+1)/3.

Combinatorial numbersand basic countin g

Binomial coefficientsC(n,m) = n!/(m!(n-m)!) (ways to pick m among n labelled elements); C(n,m)=0 if mn; C(n,0)=1; C(n,1)=n; C(n,m)=C(n,n-m):

m = 2, n = 4,5,6,... 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, n(n-1)/2; shifted triangular numbers

m = 3, n = 6,7,8,... 20, 35, 56, 84, 120, 165, 220, 286, 364, n(n-1)(n-2)/3!; shifted tetrahedral numbers

m = 4, n = 8,9,10,... 70, 126, 210, 330, 495, 715, 1001, 1365, n(n-1)(n-2)(n-3)/4!; for n < 2m, use C(n,n-m)

m = 5, n = 10,11,12... 252, 462, 792, 1287, 2002, 3003, 4368, n(n-1)(n-2)(n-3)(n-4)/5!

m = 6, n = 12,13,14,... 924, 1716, 3003, 5005, 8008, 12376, n(n-1)(n-2)(n-3)(n-4)(n-5)/6! = n(6)/6!

m = 7, n = 14,15,16... 3432, 6435, 11440, 19448, 31824, n(7)/7!; all cases up to n=14 are covered

Central binomial coefficientsC(2n,n) = (2n)!/n!2 1, 2, 6, 20, 70, 252, 924, 3432, 12870, C(2n,n) = Sum[k=0,n]{C2(n,k)}: Franel numberof order 2

Factorialsn! = 1*2*3...*n 1, 1, 2, 6, 24, 120, 720, 5040, 40320, Permutations of an ordered set of n labelled elements

Quadruple factorials(2n)!/n! 1, 2, 12, 120, 1680, 30240, 665280, in terms of Catalan numbers, equal to (n+1)!C(n)

Factorionsin base 10 1, 2, 145, 40585 (that's all) Equal to the sum of factorials of their dec digits

Factorionsin base 16

1, 2, 2615428934649 (that's all)

Equal to the sum of factorials of their hex digits

Franel numbersof order 3 1, 2, 10, 56, 346, 2252, 15184, 104960, Sum[k=0,n]{C3(n,k)}

Lah numbersL(n,m) (unsigned); signed L(n,m) = (-1)nL(n,m); They expand rising factorials in terms of falling factorials and vice versa. L(n,1) = n!

m = 2, n = 2,3,4,... 1, 6, 36, 240, 1800, 15120, 141120,

m = 3, n = 3,4,5,... 1, 12, 120, 1200, 12600, 141120, General formula: L(n,m)=C(n,m)(n-1)!/(m-1)!
http://en.wikipedia.org/wiki/Hexagonal_numberhttp://en.wikipedia.org/wiki/Hexagonal_numberhttps://oeis.org/A003215https://oeis.org/A003215https://oeis.org/A003215http://en.wikipedia.org/wiki/Polygonal_numberhttp://en.wikipedia.org/wiki/Polygonal_numberhttp://oeis.org/A069099http://oeis.org/A069099http://oeis.org/A069099http://en.wikipedia.org/wiki/Centered_octagonal_numberhttp://en.wikipedia.org/wiki/Centered_octagonal_numberhttp://oeis.org/A016754http://oeis.org/A016754http://oeis.org/A016754http://en.wikipedia.org/wiki/Tetrahedral_numberhttp://en.wikipedia.org/wiki/Tetrahedral_numberhttp://oeis.org/A000292http://oeis.org/A000292http://oeis.org/A000292http://en.wikipedia.org/wiki/Cubic_numberhttp://en.wikipedia.org/wiki/Cubic_numberhttp://oeis.org/A000578http://oeis.org/A000578http://oeis.org/A000578http://en.wikipedia.org/wiki/Pentatopic_numberhttp://en.wikipedia.org/wiki/Pentatopic_numberhttps://oeis.org/A000332https://oeis.org/A000332https://oeis.org/A000332http://en.wikipedia.org/wiki/Octahedral_numberhttp://en.wikipedia.org/wiki/Octahedral_numberhttp://oeis.org/A005900http://oeis.org/A005900http://oeis.org/A005900http://en.wikipedia.org/wiki/Binomial_coefficienthttp://en.wikipedia.org/wiki/Binomial_coefficienthttp://oeis.org/A000217http://oeis.org/A000217http://oeis.org/A000217http://oeis.org/A000292http://oeis.org/A000292http://oeis.org/A000292http://oeis.org/A000332http://oeis.org/A000332http://oeis.org/A000332http://oeis.org/A000389http://oeis.org/A000389http://oeis.org/A000389http://oeis.org/A000579http://oeis.org/A000579http://oeis.org/A000579http://oeis.org/A000580http://oeis.org/A000580http://oeis.org/A000580https://oeis.org/A000984https://oeis.org/A000984https://oeis.org/A000984http://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Factorialhttps://oeis.org/A000142https://oeis.org/A000142https://oeis.org/A000142https://oeis.org/A001813https://oeis.org/A001813https://oeis.org/A001813http://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttp://mathworld.wolfram.com/FranelNumber.htmlhttp://mathworld.wolfram.com/FranelNumber.htmlhttps://oeis.org/A000172https://oeis.org/A000172https://oeis.org/A000172http://en.wikipedia.org/wiki/Lah_numberhttp://en.wikipedia.org/wiki/Lah_numberhttps://oeis.org/A001286https://oeis.org/A001286https://oeis.org/A001286https://oeis.org/A001754https://oeis.org/A001754https://oeis.org/A001754https://oeis.org/A001754https://oeis.org/A001286http://en.wikipedia.org/wiki/Lah_numberhttps://oeis.org/A000172http://mathworld.wolfram.com/FranelNumber.htmlhttp://en.wikipedia.org/wiki/Factorionhttp://en.wikipedia.org/wiki/Factorionhttps://oeis.org/A001813https://oeis.org/A000142http://en.wikipedia.org/wiki/Factorialhttps://oeis.org/A000984http://oeis.org/A000580http://oeis.org/A000579http://oeis.org/A000389http://oeis.org/A000332http://oeis.org/A000292http://oeis.org/A000217http://en.wikipedia.org/wiki/Binomial_coefficienthttp://oeis.org/A005900http://en.wikipedia.org/wiki/Octahedral_numberhttps://oeis.org/A000332http://en.wikipedia.org/wiki/Pentatopic_numberhttp://oeis.org/A000578http://en.wikipedia.org/wiki/Cubic_numberhttp://oeis.org/A000292http://en.wikipedia.org/wiki/Tetrahedral_numberhttp://oeis.org/A016754http://en.wikipedia.org/wiki/Centered_octagonal_numberhttp://oeis.org/A069099http://en.wikipedia.org/wiki/Polygonal_numberhttps://oeis.org/A003215http://en.wikipedia.org/wiki/Hexagonal_number


11/25

m = 4, n = 4,5,6,... 1, 20, 300, 4200, 58800, 846720,

Stirling numbers of the first kindc(n,m) (unsigned); signed s(n,m) = (-1)n-mc(n,m); number of permutations of n distinct elements with exactly m cycles.

m = 1, n = 1,2,3,... 1, 1, 2, 6, 24, 120, 720, 5040, 40320, (n-1)! Note: by convention, c(n,0) = 1

m = 2, n = 2,3,4,... 1, 3, 11, 50, 274, 1764, 13068, 109584, a(n+1)=n*a(n)+(n-1)!

m = 3, n = 3,4,5,... 1, 6, 35, 225, 1624, 13132, 118124,

m = 4, n = 4,5,6,... 1, 10, 85, 735, 6769, 67284, 723680, A definition of s(n,m):

m = 5, n = 5,6,7,... 1, 15, 175, 1960, 22449, 269325, x(n)= x(x-1)(x-2)...(x-(n-1)) = Sum[m=0..n]{s(n,m).xm}

m = 6, n = 6,7,8,... 1, 21, 322, 4536, 63273, 902055, See also OEISA008275

m = 7, n = 7,8,9,... 1, 28, 546, 9450, 157773, 2637558,

m = 8, n = 8,9,10,... 1, 36, 870, 18150, 357423, 6926634, ...

m = 9, n = 9,10,11,... 1, 45, 1320, 32670, 749463, 16669653, ...

Stirling numbers of the second kindS(n,m); number of partitions of n distinct elements into m non-empty subsets. S(n,1) = 1. By convention, S(0,0) = 1.

m = 2, n = 2,3,4,... 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2(n-1)-1

m = 3, n = 3,4,5,... 1, 6, 25, 90, 301, 966, 3025, 9330,

m = 4, n = 4,5,6,... 1, 10, 65, 350, 1701, 7770, 34105, A definition of S(n,m):

m = 5, n = 5,6,7,... 1, 15, 140, 1050, 6951, 42525, 246730, xn= Sum[m=0..n]{S(n,m).x(m)}

m = 6, n = 6,7,8,... 1, 21, 266, 2646, 22827, 179487, See also OEISA008277

m = 7, n = 7,8,9,... 1, 28, 462, 5880, 63987, 627396,

m = 8, n = 8,9,10,... 1, 36, 750, 11880, 159027, 1899612,

m = 9, n = 9,10,11,... 1, 45, 1155, 22275, 359502, 5135130,

Morecountin g (enumeration) of various objects

Subsetsof a set of n labelled elements 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2n, for n=0,1,2,...

Composition numbers 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1 for n=0, else 2^(n-1); Distinct compositions of number n=0,1,2,...

Catalan numbersC(n) 1, 1, 2, 5, 14, 42, 132, 429,1430,4862, C(n) = C(2n,n)/(n+1); ubiquitous in number theory

Bell numbersB(n) 1, 1, 2, 5, 15, 52, 203, 877, 4140, Partitions of a set of n=0,1,2,... labelled elements
https://oeis.org/A001755https://oeis.org/A001755https://oeis.org/A001755http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.htmlhttp://mathworld.wolfram.com/StirlingNumberoftheFirstKind.htmlhttp://oeis.org/A000142http://oeis.org/A000142http://oeis.org/A000142http://oeis.org/A000254http://oeis.org/A000254http://oeis.org/A000254http://oeis.org/A000399http://oeis.org/A000399http://oeis.org/A000399http://oeis.org/A000454http://oeis.org/A000454http://oeis.org/A000454http://oeis.org/A000482http://oeis.org/A000482http://oeis.org/A000482http://oeis.org/A001233http://oeis.org/A001233http://oeis.org/A001233https://oeis.org/A008275https://oeis.org/A008275https://oeis.org/A008275http://oeis.org/A001234http://oeis.org/A001234http://oeis.org/A001234http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kindhttp://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kindhttps://oeis.org/A000225https://oeis.org/A000225https://oeis.org/A000225http://oeis.org/A000392http://oeis.org/A000392http://oeis.org/A000392http://oeis.org/A000453http://oeis.org/A000453http://oeis.org/A000453http://oeis.org/A000481http://oeis.org/A000481http://oeis.org/A000481http://oeis.org/A000770http://oeis.org/A000770http://oeis.org/A000770https://oeis.org/A008277https://oeis.org/A008277https://oeis.org/A008277http://oeis.org/A000771http://oeis.org/A000771http://oeis.org/A000771https://oeis.org/A049434https://oeis.org/A049434https://oeis.org/A049434https://oeis.org/A049447https://oeis.org/A049447https://oeis.org/A049447https://oeis.org/A000079https://oeis.org/A000079https://oeis.org/A000079http://en.wikipedia.org/wiki/Composition_(number_theory)#Number_of_compositionshttp://en.wikipedia.org/wiki/Composition_(number_theory)#Number_of_compositionshttps://oeis.org/A011782https://oeis.org/A011782https://oeis.org/A011782http://en.wikipedia.org/wiki/Catalan_numberhttp://en.wikipedia.org/wiki/Catalan_numberhttps://oeis.org/A000108https://oeis.org/A000108https://oeis.org/A000108http://en.wikipedia.org/wiki/Bell_numberhttp://en.wikipedia.org/wiki/Bell_numberhttps://oeis.org/A000110https://oeis.org/A000110https://oeis.org/A000110https://oeis.org/A000110http://en.wikipedia.org/wiki/Bell_numberhttps://oeis.org/A000108http://en.wikipedia.org/wiki/Catalan_numberhttps://oeis.org/A011782http://en.wikipedia.org/wiki/Composition_(number_theory)#Number_of_compositionshttps://oeis.org/A000079https://oeis.org/A049447https://oeis.org/A049434http://oeis.org/A000771https://oeis.org/A008277http://oeis.org/A000770http://oeis.org/A000481http://oeis.org/A000453http://oeis.org/A000392https://oeis.org/A000225http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kindhttp://oeis.org/A001234https://oeis.org/A008275http://oeis.org/A001233http://oeis.org/A000482http://oeis.org/A000454http://oeis.org/A000399http://oeis.org/A000254http://oeis.org/A000142http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.htmlhttps://oeis.org/A001755


12/25

Ordered Bell numbersor Fubini numbers 1, 1, 3, 13, 75, 541, 4683, 47293, Weakly ordered partitions of n=0,1,2,... labelled elements

Partition numbersp(n) 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, Partitions of a set of n=0,1,2,... unlabelled elements

Free labelledtrees 1, 1, 3, 16, 125, 1296,16807,262144, nn-2(Cayley formula), n=1,2,3,... labelled vertices

Rooted labelled trees 1, 2, 9, 64, 625, 7776, 117649, nn-1, n=1,2,3,... labelled vertices

Free unlabelled trees 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235 for n=1,2,3,... unlabeled vertices

Rooted unlabelled trees 1, 2, 4, 9, 20, 48, 115, 286, 719, for n=1,2,3,... unlabelled vertices

Simple connected graphs 1, 1, 2, 6, 21, 112, 853, 11117, 261080, for n = 1,2,3,... unlabelled nodes

Composition s of powers of integer numbers

Pythagorean triples(a,b,c), a2+ b2= c2 (3,4,5) (5,12,13) (7,24,25) (8,15,17) (9,40,41) (11,60,61) (12,35,37) (13,84,85) (16,63,65) ...

Pythagorean quadruples,a2+ b2+ c2= d2 (1,2,2,3) (2,3,6,7) (4,4,7,9) (1,4,8,9) (6,6,7,11) (2,6,9,11) (10,10,23,27) (7,14,22,23) ...

Pythagorean quintuples (1,2,4,10,11) (1,2,8,10,13) ... etc; there is an infinity of them in each category

Taxicab numbersTa(1), Ta(2), Ta(3), Ta(4),

Ta(5),Ta(6)

2, 1729, 87539319, 6963472309248,

48988659276962496,24153319581254312065344,

Ta(n) is the smallest T(n) number, one that can be written as a

sum of two positive cubes in n different ways. Only six are knownand only Ta(1), Ta(2) are cubefree(not divisible by a cube).

Special numbers related to divisors; (n) is thedivisor function(sum of all divisors of n), and (n)-n is the sum of all proper divisorsof n

Perfect numbers 6, 28, 496, 8128, 33550336, n = equals the sum of its own proper divisors = (n) - n

Abundant numbers 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, n exceeds the sum of its own proper divisors; n > (n) - n

Deficient numbers 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, n is less than the sum of its own proper divisors; n < (n) - n

Odd abundant numbers 945, 1575, 2205, 2835, 3465, 4095, Funny the smallest one is so large

Odd abundant numbers not divisible by 3 5391411025, 26957055125, see also

Amicable number pairs (220,284); (1184,1210); (2620,2924); n = (m) - m, m = (n) - n

Superperfect numbers 2, 4, 16, 64, 4096, 65536, 262144, n = ((n)) - n

Special numbers related to absolute and/or relative primes, natural number f actorizations, etc

Prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, A prime number is divisible only by 1 and itself; excluding 1

Twin prime numbers 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, For each prime p in this list, p+2 is also a prime
http://oeis.org/A000670http://oeis.org/A000670https://oeis.org/A000670https://oeis.org/A000670https://oeis.org/A000670http://en.wikipedia.org/wiki/Partition_of_numbershttp://en.wikipedia.org/wiki/Partition_of_numbershttps://oeis.org/A000041https://oeis.org/A000041https://oeis.org/A000041http://en.wikipedia.org/wiki/Tree_(graph_theory)http://en.wikipedia.org/wiki/Tree_(graph_theory)http://en.wikipedia.org/wiki/Tree_(graph_theory)https://oeis.org/A000272https://oeis.org/A000272https://oeis.org/A000272https://oeis.org/A000169https://oeis.org/A000169https://oeis.org/A000169http://oeis.org/A000055http://oeis.org/A000055http://oeis.org/A000055http://oeis.org/A000081http://oeis.org/A000081http://oeis.org/A000081https://oeis.org/A001349https://oeis.org/A001349https://oeis.org/A001349http://en.wikipedia.org/wiki/Pythagorean_triplehttp://en.wikipedia.org/wiki/Pythagorean_triplehttp://mathworld.wolfram.com/PythagoreanQuadruple.htmlhttp://mathworld.wolfram.com/PythagoreanQuadruple.htmlhttp://en.wikipedia.org/wiki/Taxicab_numberhttp://en.wikipedia.org/wiki/Taxicab_numberhttps://oeis.org/A011541https://oeis.org/A011541https://oeis.org/A011541http://en.wikipedia.org/wiki/Perfect_numberhttp://en.wikipedia.org/wiki/Perfect_numberhttps://oeis.org/A000396https://oeis.org/A000396https://oeis.org/A000396http://en.wikipedia.org/wiki/Abundant_numbershttp://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005101https://oeis.org/A005101https://oeis.org/A005101http://en.wikipedia.org/wiki/Abundant_numbershttp://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005100https://oeis.org/A005100https://oeis.org/A005100http://en.wikipedia.org/wiki/Abundant_numbershttp://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005231https://oeis.org/A005231https://oeis.org/A005231http://en.wikipedia.org/wiki/Abundant_numbershttp://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A115414https://oeis.org/A115414https://oeis.org/A115414https://oeis.org/A047802https://oeis.org/A047802http://en.wikipedia.org/wiki/Amicable_numbershttp://en.wikipedia.org/wiki/Amicable_numbershttp://oeis.org/A063990http://oeis.org/A063990http://oeis.org/A063990http://en.wikipedia.org/wiki/Superperfect_numberhttp://en.wikipedia.org/wiki/Superperfect_numberhttps://oeis.org/A019279https://oeis.org/A019279https://oeis.org/A019279http://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttps://oeis.org/A000040https://oeis.org/A000040https://oeis.org/A000040http://en.wikipedia.org/wiki/Twin_primehttp://en.wikipedia.org/wiki/Twin_primehttp://oeis.org/A077800http://oeis.org/A077800http://oeis.org/A077800http://oeis.org/A077800http://en.wikipedia.org/wiki/Twin_primehttps://oeis.org/A000040http://en.wikipedia.org/wiki/Prime_numberhttps://oeis.org/A019279http://en.wikipedia.org/wiki/Superperfect_numberhttp://oeis.org/A063990http://en.wikipedia.org/wiki/Amicable_numbershttps://oeis.org/A047802https://oeis.org/A115414http://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005231http://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005100http://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A005101http://en.wikipedia.org/wiki/Abundant_numbershttps://oeis.org/A000396http://en.wikipedia.org/wiki/Perfect_numberhttps://oeis.org/A011541http://en.wikipedia.org/wiki/Taxicab_numberhttp://mathworld.wolfram.com/PythagoreanQuadruple.htmlhttp://en.wikipedia.org/wiki/Pythagorean_triplehttps://oeis.org/A001349http://oeis.org/A000081http://oeis.org/A000055https://oeis.org/A000169https://oeis.org/A000272http://en.wikipedia.org/wiki/Tree_(graph_theory)https://oeis.org/A000041http://en.wikipedia.org/wiki/Partition_of_numbershttps://oeis.org/A000670http://oeis.org/A000670


13/25

Euler's totient function(n) for n=1,2,3,... 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, Number of k's smaller than n and relatively prime to it

Mbius function(n) for n=1,2,3,... 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, (n) = (-1)^k if n has k different prime factors; else (n) = 0

Mersenne primes(first 7 for p = 2,3,5,7,13,17,19) 3, 7, 31, 127, 8191, 131071, 524287, Some M(p) = 2p-1; p prime;Largest known:M(43112609)

Pseudoprimesto base 2 (Sarrus numbers) 341, 561, 645, 1105, 1387, 1729, Composite odd n such that 2n-1= 1 (mod n)

Pseudoprimesto base 3 91, 121, 286, 671, 703, 949, 1105, Composite odd n such that 3n-1= 1 (mod n)

Carmichael's pseudoprimes 561, 1105, 1729, 2465, 2821, 6601, Composite odd n such that bn-1= 1 (mod n) for any coprime b

Euler's pseudoprimesin base 2 341, 561, 1105, 1729, 1905, 2047, Composite odd n such that 2 (n-1)/2= 1 (mod n)

Named sequencesof binary numbers {0,1} or {-1,+1}.

Baum - Sweet sequence 1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0 1 if binary(n) contains no block of 0's of odd length

Fibonacci words 0, 01, 010, 01001, 01001010, ... Like Fibonacci recurrence, but using string concatenation

Infinite Fibonacci word 010010100100101001010010010 Infinite continuation of the above

Golay - Rudin - Shapiro sequence +1,+1,+1,-1,+1,+1,-1,+1,+1,+1,+1,-1 (-1)^Sum[i]{didi+1}

Thue - Morse sequence 0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0 1 if binary(n) contains an odd number of ones (parity= 1)

Other named sequencesof integers

Belphegor numbersB(n), n=0,1,2,.. 16661, 1066601, 100666001, prime for n=0, 13, 42, 506, 608, 2472, 2623, 28291,

Euler numbersE(n) for n=0,2,4,... 1, -1, 5, -61, 1385, -50521, 2702765, 1/cosh(t) = Sum[n=0..]{tn(E(n)/n!)}; the odd ones are 0

Fibonacci numbersF(n) 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, Fn= Fn-1+ Fn-2; F0= 0, F1= 1

Golomb's sequence (or Silverman's sequence) 1, 2,2, 3,3, 4,4,4, 5,5,5, 6,6,6,6, 7,7,7 a(1)=1, a(n)= least number of times n occurs if a(n)1, Bm= m,0- Sum[k=0..(m-1)]{C(m,k)Bk/(m-k+1)}; x/(ex-1) = Sum[k=0,1,..]{Bnxn/n!}; Example: B10= 5/66

Bn= N/D; n = 2,4,6,... N: 1,-1, 1, -1, 5, -691, 7, -3617, 43867, D: 6, 30, 42, 30, 66, 2730, 6, 510, 798,

Other
http://mathworld.wolfram.com/TotientFunction.htmlhttp://mathworld.wolfram.com/TotientFunction.htmlhttp://oeis.org/A000010http://oeis.org/A000010http://oeis.org/A000010http://mathworld.wolfram.com/TotientFunction.htmlhttp://mathworld.wolfram.com/TotientFunction.htmlhttp://oeis.org/A008683http://oeis.org/A008683http://oeis.org/A008683http://en.wikipedia.org/wiki/Mersenne_numbers#List_of_known_Mersenne_primeshttp://en.wikipedia.org/wiki/Mersenne_numbers#List_of_known_Mersenne_primeshttp://oeis.org/A000668http://oeis.org/A000668http://oeis.org/A000668http://www.mersenne.org/http://www.mersenne.org/http://www.mersenne.org/http://mathworld.wolfram.com/FermatPseudoprime.htmlhttp://mathworld.wolfram.com/FermatPseudoprime.htmlhttp://oeis.org/A001567http://oeis.org/A001567http://oeis.org/A001567http://mathworld.wolfram.com/FermatPseudoprime.htmlhttp://mathworld.wolfram.com/FermatPseudoprime.htmlhttp://oeis.org/A005935http://oeis.org/A005935http://oeis.org/A005935http://mathworld.wolfram.com/CarmichaelNumber.htmlhttp://mathworld.wolfram.com/CarmichaelNumber.htmlhttp://oeis.org/A002997http://oeis.org/A002997http://oeis.org/A002997http://mathworld.wolfram.com/EulerPseudoprime.htmlhttp://mathworld.wolfram.com/EulerPseudoprime.htmlhttp://oeis.org/A006970http://oeis.org/A006970http://oeis.org/A006970http://en.wikipedia.org/wiki/Baum%E2%80%93Sweet_sequencehttp://en.wikipedia.org/wiki/Baum%E2%80%93Sweet_sequencehttps://oeis.org/A086747https://oeis.org/A086747https://oeis.org/A086747http://en.wikipedia.org/wiki/Fibonacci_wordhttp://en.wikipedia.org/wiki/Fibonacci_wordhttp://en.wikipedia.org/wiki/Fibonacci_wordhttp://en.wikipedia.org/wiki/Fibonacci_wordhttp://oeis.org/A003849http://oeis.org/A003849http://oeis.org/A003849http://en.wikipedia.org/wiki/Rudin%E2%80%93Shapiro_sequencehttp://en.wikipedia.org/wiki/Rudin%E2%80%93Shapiro_sequencehttps://oeis.org/A020985https://oeis.org/A020985https://oeis.org/A020985http://en.wikipedia.org/wiki/Thue-Morse_sequencehttp://en.wikipedia.org/wiki/Thue-Morse_sequencehttps://oeis.org/A010060https://oeis.org/A010060https://oeis.org/A010060https://oeis.org/A232449https://oeis.org/A232449https://oeis.org/A232449https://oeis.org/A232448https://oeis.org/A232448https://oeis.org/A232448http://en.wikipedia.org/wiki/Euler_numberhttp://en.wikipedia.org/wiki/Euler_numberhttps://oeis.org/A028296https://oeis.org/A028296https://oeis.org/A028296http://en.wikipedia.org/wiki/Fibonacci_numberhttp://en.wikipedia.org/wiki/Fibonacci_numberhttps://oeis.org/A000045https://oeis.org/A000045https://oeis.org/A000045http://en.wikipedia.org/wiki/Golomb_sequencehttp://en.wikipedia.org/wiki/Golomb_sequencehttps://oeis.org/A001462https://oeis.org/A001462https://oeis.org/A001462http://en.wikipedia.org/wiki/Lucas_numberhttp://en.wikipedia.org/wiki/Lucas_numberhttps://oeis.org/A000032https://oeis.org/A000032https://oeis.org/A000032http://en.wikipedia.org/wiki/Sylvester%27s_sequencehttp://en.wikipedia.org/wiki/Sylvester%27s_sequencehttps://oeis.org/A000058https://oeis.org/A000058https://oeis.org/A000058http://mathworld.wolfram.com/BernoulliNumber.htmlhttp://mathworld.wolfram.com/BernoulliNumber.htmlhttp://oeis.org/A027641http://oeis.org/A027641http://oeis.org/A027641http://oeis.org/A027642http://oeis.org/A027642http://oeis.org/A027642http://oeis.org/A027642http://oeis.org

Documents

List of Mathematical Constants