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 600579:
 600579 + 975006 step 1: 1575585 + 5855751 step 2: 7431336 + 6331347 step 3: 13762683 + 38626731 step 4: 52389414 + 41498325 step 5: 93887739 + 93778839 step 6: 187666578 + 875666781 step 7: 1063333359 + 9533333601 step 8: 10596666960 + 06966669501 step 9: 17563336461 + 16463336571 step 10: 34026673032 + 23037662043 step 11: 57064335075 + 57053346075 step 12: 114117681150 + 051186711411 step 13: 165304392561 + 165293403561 step 14: 330597796122 + 221697795033 step 15: 552295591155 + 551195592255 step 16: 1103491183410 + 0143811943011 step 17: 1247303126421 + 1246213037421 step 18: 2493516163842 + 2483616153942 step 19: 4977132317784 + 4877132317794 step 20: 9854264635578 + 8755364624589 step 21: 18609629260167 + 76106292690681 step 22: 94715921950848 + 84805912951749 step 23: 179521834902597 + 795209438125971 step 24: 974731273028568 + 865820372137479 step 25: 1840551645166047 + 7406615461550481 step 26: 9247167106716528 + 8256176017617429 step 27: 17503343124333957 + 75933342134330571 step 28: 93436685258664528 + 82546685258663439 step 29: 175983370517327967 + 769723715073389571 step 30: 945707085590717538 + 835717095580707549 step 31: 1781424181171425087 + 7805241711814241871 step 32: 9586665892985666958 + 8596665892985666859 step 33: 18183331785971333817 + 71833317958713338181 step 34: 90016649744684671998 + 89917648644794661009 step 35: 179934298389479333007 + 700333974983892439971 step 36: 880268273373371772978 + 879277173373372862088 step 37: 1759545446746744635066 + 6605364476476445459571 step 38: 8364909923223190094637 + 7364900913223299094638 step 39: 15729810836446489189275 + 57298198464463801892751 step 40: 73028009300910291082026 + 62028019201900390082037 step 41: 135056028502810681164063 + 360461186018205820650531 step 42: 495517214521016501814594 + 495418105610125412715594 step 43: 990935320131141914530188 + 881035419141131023539099 step 44: 1871970739272272938069287 + 7829608392722729370791781 step 45: 9701579131995002308861068 + 8601688032005991319751079 step 46: 18303267164000993628612147 + 74121682639900046176230381 step 47: 92424949803901039804842528 + 82524840893010930894942429 step 48: 174949790696911970699784957 + 759487996079119696097949471 step 49: 934437786776031666797734428 + 824437797666130677687734439 step 50: 1758875584442162344485468867 + 7688645844432612444855788571 step 51: 9447521428874774789341257438 + 8347521439874774788241257449 step 52: 17795042868749549577582514887 + 78841528577594594786824059771 step 53: 96636571446344144364406574658 + 85647560446344144364417563669 step 54: 182284131892688288728824138327 + 723831428827882886298131482281 step 55: 906115560720571175026955620608 + 806026559620571175027065511609 step 56: 1712142120341142350054021132217 + 7122311204500532411430212412171 step 57: 8834453324841674761484233544388
600579 takes 57 iterations / steps to resolve into a 31 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 2,439,465 times since Saturday, March 9th, 2002.)