1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, go back to step 2 and repeat.
Let's view this Reverse and Add sequence starting with 10677:
 10677 + 77601 step 1: 88278 + 87288 step 2: 175566 + 665571 step 3: 841137 + 731148 step 4: 1572285 + 5822751 step 5: 7395036 + 6305937 step 6: 13700973 + 37900731 step 7: 51601704 + 40710615 step 8: 92312319 + 91321329 step 9: 183633648 + 846336381 step 10: 1029970029 + 9200799201 step 11: 10230769230 + 03296703201 step 12: 13527472431 + 13427472531 step 13: 26954944962 + 26944945962 step 14: 53899890924 + 42909899835 step 15: 96809790759 + 95709790869 step 16: 192519581628 + 826185915291 step 17: 1018705496919 + 9196945078101 step 18: 10215650575020 + 02057505651201 step 19: 12273156226221 + 12262265137221 step 20: 24535421363442 + 24436312453542 step 21: 48971733816984 + 48961833717984 step 22: 97933567534968 + 86943576533979 step 23: 184877144068947 + 749860441778481 step 24: 934737585847428 + 824748585737439 step 25: 1759486171584867 + 7684851716849571 step 26: 9444337888434438 + 8344348887334449 step 27: 17788686775768887 + 78886757768688771 step 28: 96675444544457658 + 85675444544457669 step 29: 182350889088915327 + 723519880988053281 step 30: 905870770076968608 + 806869670077078509 step 31: 1712740440154047117 + 7117404510440472171 step 32: 8830144950594519288 + 8829154950594410388 step 33: 17659299901188929676 + 67692988110999295671 step 34: 85352288012188225347 + 74352288121088225358 step 35: 159704576133276450705 + 507054672331675407951 step 36: 666759248464951858656 + 656858159464842957666 step 37: 1323617407929794816322 + 2236184979297047163231 step 38: 3559802387226841979553 + 3559791486227832089553 step 39: 7119593873454674069106 + 6019604764543783959117 step 40: 13139198637998458028223 + 32282085489973689193131 step 41: 45421284127972147221354 + 45312274127972148212454 step 42: 90733558255944295433808 + 80833459244955285533709 step 43: 171567017500899580967517 + 715769085998005710765171 step 44: 887336103498905291732688 + 886237192509894301633788 step 45: 1773573296008799593366476 + 6746633959978006923753771 step 46: 8520207255986806517120247 + 7420217156086895527020258 step 47: 15940424412073702044140505 + 50504144020737021442404951 step 48: 66444568432810723486545456 + 65454568432701823486544466 step 49: 131899136865512546973089922 + 229980379645215568631998131 step 50: 361879516510728115605088053 + 350880506511827015615978163 step 51: 712760023022555131221066216 + 612660122131555220320067217 step 52: 1325420145154110351541133433 + 3343311451530114515410245231 step 53: 4668731596684224866951378664
10677 takes 53 iterations / steps to resolve into a 28 digit palindrome.

Most Delayed Palindromic Number for each digit length
(Only iteration counts for which no smaller records exist are considered. My program records only the smallest number that resolves for each distinct iteration count. For example, there are 18-digit numbers that resolve in 232 iterations, higher than the 228 iteration record shown for 18-digit numbers, but they were not recorded, as a smaller [17-digit] number already holds the record for 232 iterations.)

DigitsNumberResult
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
89
187
1,297
10,911
150,296
9,008,299
10,309,988
140,669,390
1,005,499,526
10,087,799,570
100,001,987,765
1,600,005,969,190
14,104,229,999,995
100,120,849,299,260
1,030,020,097,997,900
10,442,000,392,399,960
170,500,000,303,619,996
1,186,060,307,891,929,990
solves in 24 iterations.
solves in 23 iterations.
solves in 21 iterations.
solves in 55 iterations.
solves in 64 iterations.
solves in 96 iterations.
solves in 95 iterations.
solves in 98 iterations.
solves in 109 iterations.
solves in 149 iterations.
solves in 143 iterations.
solves in 188 iterations.
solves in 182 iterations.
solves in 201 iterations.
solves in 197 iterations.
solves in 236 iterations.
solves in 228 iterations.
solves in 261 iterations - World Record!
[View all records]

This reverse and add program was created by Jason Doucette.
Please visit my Palindromes and World Records page.
You have permission to use the data from this webpage (with due credit).
A link to my website is much appreciated. Thank you.

(This program has been run 2,075,454 times since Saturday, March 9th, 2002.)