Making Numbers into Palindromic Numbers

Date: 10/11/95 at 15:20:15From: AnonymousSubject: palindromes

I'm interested in palindromic numbers. Apparently almost any number can be made into a palindromic number by reversing the digits and adding and then repeating the steps until you get a palindromic number. Some require many steps. I'm wondering if there is a list anywhere that tells which numbers can be made into palindromic sums and how many steps would be required. I'm interested in getting a list for numbers <1000 although I'd be happy to get a list for those <100. Do you know where I might getsuch a list?

Date: 11/29/95 at 12:20:10From: Doctor KenSubject: Re: palindromes

Hello!

As far as I know, your question is an unanswered one in the general case, i.e. people don't know whether it's true for all numbers or not. But I think people have checked the first few cases, and they all work.

I wrote a little program using the language PERL that checks all the numbers up to 200. Here's what it told me:

1 gets palindromic after 0 steps: 12 gets palindromic after 0 steps: 23 gets palindromic after 0 steps: 34 gets palindromic after 0 steps: 45 gets palindromic after 0 steps: 56 gets palindromic after 0 steps: 67 gets palindromic after 0 steps: 78 gets palindromic after 0 steps: 89 gets palindromic after 0 steps: 910 gets palindromic after 1 steps: 1111 gets palindromic after 0 steps: 1112 gets palindromic after 1 steps: 3313 gets palindromic after 1 steps: 4414 gets palindromic after 1 steps: 5515 gets palindromic after 1 steps: 6616 gets palindromic after 1 steps: 7717 gets palindromic after 1 steps: 8818 gets palindromic after 1 steps: 9919 gets palindromic after 2 steps: 12120 gets palindromic after 1 steps: 2221 gets palindromic after 1 steps: 3322 gets palindromic after 0 steps: 2223 gets palindromic after 1 steps: 5524 gets palindromic after 1 steps: 6625 gets palindromic after 1 steps: 7726 gets palindromic after 1 steps: 8827 gets palindromic after 1 steps: 9928 gets palindromic after 2 steps: 12129 gets palindromic after 1 steps: 12130 gets palindromic after 1 steps: 3331 gets palindromic after 1 steps: 4432 gets palindromic after 1 steps: 5533 gets palindromic after 0 steps: 3334 gets palindromic after 1 steps: 7735 gets palindromic after 1 steps: 88

36 gets palindromic after 1 steps: 9937 gets palindromic after 2 steps: 12138 gets palindromic after 1 steps: 12139 gets palindromic after 2 steps: 36340 gets palindromic after 1 steps: 4441 gets palindromic after 1 steps: 5542 gets palindromic after 1 steps: 6643 gets palindromic after 1 steps: 7744 gets palindromic after 0 steps: 4445 gets palindromic after 1 steps: 9946 gets palindromic after 2 steps: 12147 gets palindromic after 1 steps: 12148 gets palindromic after 2 steps: 36349 gets palindromic after 2 steps: 48450 gets palindromic after 1 steps: 5551 gets palindromic after 1 steps: 6652 gets palindromic after 1 steps: 7753 gets palindromic after 1 steps: 8854 gets palindromic after 1 steps: 9955 gets palindromic after 0 steps: 5556 gets palindromic after 1 steps: 12157 gets palindromic after 2 steps: 36358 gets palindromic after 2 steps: 48459 gets palindromic after 3 steps: 111160 gets palindromic after 1 steps: 6661 gets palindromic after 1 steps: 7762 gets palindromic after 1 steps: 8863 gets palindromic after 1 steps: 9964 gets palindromic after 2 steps: 12165 gets palindromic after 1 steps: 12166 gets palindromic after 0 steps: 6667 gets palindromic after 2 steps: 48468 gets palindromic after 3 steps: 111169 gets palindromic after 4 steps: 488470 gets palindromic after 1 steps: 7771 gets palindromic after 1 steps: 8872 gets palindromic after 1 steps: 9973 gets palindromic after 2 steps: 12174 gets palindromic after 1 steps: 12175 gets palindromic after 2 steps: 36376 gets palindromic after 2 steps: 48477 gets palindromic after 0 steps: 7778 gets palindromic after 4 steps: 488479 gets palindromic after 6 steps: 4404480 gets palindromic after 1 steps: 8881 gets palindromic after 1 steps: 9982 gets palindromic after 2 steps: 12183 gets palindromic after 1 steps: 12184 gets palindromic after 2 steps: 36385 gets palindromic after 2 steps: 48486 gets palindromic after 3 steps: 111187 gets palindromic after 4 steps: 488488 gets palindromic after 0 steps: 8889 gets palindromic after 24 steps: 881320002318890 gets palindromic after 1 steps: 9991 gets palindromic after 2 steps: 12192 gets palindromic after 1 steps: 12193 gets palindromic after 2 steps: 36394 gets palindromic after 2 steps: 48495 gets palindromic after 3 steps: 111196 gets palindromic after 4 steps: 488497 gets palindromic after 6 steps: 4404498 gets palindromic after 24 steps: 881320002318899 gets palindromic after 0 steps: 99100 gets palindromic after 1 steps: 101101 gets palindromic after 0 steps: 101102 gets palindromic after 1 steps: 303

103 gets palindromic after 1 steps: 404104 gets palindromic after 1 steps: 505105 gets palindromic after 1 steps: 606106 gets palindromic after 1 steps: 707106 gets palindromic after 1 steps: 707107 gets palindromic after 1 steps: 808108 gets palindromic after 1 steps: 909109 gets palindromic after 2 steps: 1111110 gets palindromic after 1 steps: 121111 gets palindromic after 0 steps: 111112 gets palindromic after 1 steps: 323113 gets palindromic after 1 steps: 424114 gets palindromic after 1 steps: 525115 gets palindromic after 1 steps: 626116 gets palindromic after 1 steps: 727117 gets palindromic after 1 steps: 828118 gets palindromic after 1 steps: 929119 gets palindromic after 2 steps: 1331120 gets palindromic after 1 steps: 141121 gets palindromic after 0 steps: 121122 gets palindromic after 1 steps: 343123 gets palindromic after 1 steps: 444124 gets palindromic after 1 steps: 545125 gets palindromic after 1 steps: 646126 gets palindromic after 1 steps: 747127 gets palindromic after 1 steps: 848128 gets palindromic after 1 steps: 949129 gets palindromic after 2 steps: 1551130 gets palindromic after 1 steps: 161131 gets palindromic after 0 steps: 131132 gets palindromic after 1 steps: 363133 gets palindromic after 1 steps: 464134 gets palindromic after 1 steps: 565135 gets palindromic after 1 steps: 666136 gets palindromic after 1 steps: 767137 gets palindromic after 1 steps: 868138 gets palindromic after 1 steps: 969139 gets palindromic after 2 steps: 1771140 gets palindromic after 1 steps: 181141 gets palindromic after 0 steps: 141142 gets palindromic after 1 steps: 383143 gets palindromic after 1 steps: 484144 gets palindromic after 1 steps: 585145 gets palindromic after 1 steps: 686146 gets palindromic after 1 steps: 787147 gets palindromic after 1 steps: 888148 gets palindromic after 1 steps: 989149 gets palindromic after 2 steps: 1991150 gets palindromic after 2 steps: 303151 gets palindromic after 0 steps: 151152 gets palindromic after 2 steps: 707153 gets palindromic after 2 steps: 909154 gets palindromic after 2 steps: 1111155 gets palindromic after 3 steps: 4444156 gets palindromic after 3 steps: 6666157 gets palindromic after 3 steps: 8888158 gets palindromic after 3 steps: 11011159 gets palindromic after 2 steps: 1221160 gets palindromic after 2 steps: 343161 gets palindromic after 0 steps: 161162 gets palindromic after 2 steps: 747163 gets palindromic after 2 steps: 949164 gets palindromic after 3 steps: 2662165 gets palindromic after 3 steps: 4884166 gets palindromic after 5 steps: 45254167 gets palindromic after 11 steps: 88555588168 gets palindromic after 3 steps: 13431

169 gets palindromic after 2 steps: 1441170 gets palindromic after 2 steps: 383171 gets palindromic after 0 steps: 171172 gets palindromic after 2 steps: 787173 gets palindromic after 2 steps: 989174 gets palindromic after 4 steps: 5115175 gets palindromic after 4 steps: 9559176 gets palindromic after 5 steps: 44044177 gets palindromic after 15 steps: 8836886388178 gets palindromic after 3 steps: 15851179 gets palindromic after 2 steps: 1661180 gets palindromic after 3 steps: 747181 gets palindromic after 0 steps: 181182 gets palindromic after 6 steps: 45254183 gets palindromic after 4 steps: 13431184 gets palindromic after 3 steps: 2552185 gets palindromic after 3 steps: 4774185 gets palindromic after 3 steps: 4774186 gets palindromic after 3 steps: 6996187 gets palindromic after 23 steps: 8813200023188188 gets palindromic after 7 steps: 233332189 gets palindromic after 2 steps: 1881190 gets palindromic after 7 steps: 45254191 gets palindromic after 0 steps: 191192 gets palindromic after 4 steps: 6996193 gets palindromic after 8 steps: 233332194 gets palindromic after 3 steps: 2992195 gets palindromic after 4 steps: 9339197 gets palindromic after 7 steps: 881188198 gets palindromic after 5 steps: 79497199 gets palindromic after 3 steps: 3113200 gets palindromic after 1 steps: 202