# 山水娱乐

•  REVERSAL-ADDITION PALINDROME TEST ON 147996

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 147996:
 147996 + 699741 step 1: 847737 + 737748 step 2: 1585485 + 5845851 step 3: 7431336 + 6331347 step 4: 13762683 + 38626731 step 5: 52389414 + 41498325 step 6: 93887739 + 93778839 step 7: 187666578 + 875666781 step 8: 1063333359 + 9533333601 step 9: 10596666960 + 06966669501 step 10: 17563336461 + 16463336571 step 11: 34026673032 + 23037662043 step 12: 57064335075 + 57053346075 step 13: 114117681150 + 051186711411 step 14: 165304392561 + 165293403561 step 15: 330597796122 + 221697795033 step 16: 552295591155 + 551195592255 step 17: 1103491183410 + 0143811943011 step 18: 1247303126421 + 1246213037421 step 19: 2493516163842 + 2483616153942 step 20: 4977132317784 + 4877132317794 step 21: 9854264635578 + 8755364624589 step 22: 18609629260167 + 76106292690681 step 23: 94715921950848 + 84805912951749 step 24: 179521834902597 + 795209438125971 step 25: 974731273028568 + 865820372137479 step 26: 1840551645166047 + 7406615461550481 step 27: 9247167106716528 + 8256176017617429 step 28: 17503343124333957 + 75933342134330571 step 29: 93436685258664528 + 82546685258663439 step 30: 175983370517327967 + 769723715073389571 step 31: 945707085590717538 + 835717095580707549 step 32: 1781424181171425087 + 7805241711814241871 step 33: 9586665892985666958 + 8596665892985666859 step 34: 18183331785971333817 + 71833317958713338181 step 35: 90016649744684671998 + 89917648644794661009 step 36: 179934298389479333007 + 700333974983892439971 step 37: 880268273373371772978 + 879277173373372862088 step 38: 1759545446746744635066 + 6605364476476445459571 step 39: 8364909923223190094637 + 7364900913223299094638 step 40: 15729810836446489189275 + 57298198464463801892751 step 41: 73028009300910291082026 + 62028019201900390082037 step 42: 135056028502810681164063 + 360461186018205820650531 step 43: 495517214521016501814594 + 495418105610125412715594 step 44: 990935320131141914530188 + 881035419141131023539099 step 45: 1871970739272272938069287 + 7829608392722729370791781 step 46: 9701579131995002308861068 + 8601688032005991319751079 step 47: 18303267164000993628612147 + 74121682639900046176230381 step 48: 92424949803901039804842528 + 82524840893010930894942429 step 49: 174949790696911970699784957 + 759487996079119696097949471 step 50: 934437786776031666797734428 + 824437797666130677687734439 step 51: 1758875584442162344485468867 + 7688645844432612444855788571 step 52: 9447521428874774789341257438 + 8347521439874774788241257449 step 53: 17795042868749549577582514887 + 78841528577594594786824059771 step 54: 96636571446344144364406574658 + 85647560446344144364417563669 step 55: 182284131892688288728824138327 + 723831428827882886298131482281 step 56: 906115560720571175026955620608 + 806026559620571175027065511609 step 57: 1712142120341142350054021132217 + 7122311204500532411430212412171 step 58: 8834453324841674761484233544388
147996 takes 58 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 2,061,618 times since Saturday, March 9th, 2002.)