REVERSAL-ADDITION PALINDROME TEST ON 178992

Reverse and Add Process:

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 178992:
178992
+ 299871
step 1: 478863
+ 368874
step 2: 847737
+ 737748
step 3: 1585485
+ 5845851
step 4: 7431336
+ 6331347
step 5: 13762683
+ 38626731
step 6: 52389414
+ 41498325
step 7: 93887739
+ 93778839
step 8: 187666578
+ 875666781
step 9: 1063333359
+ 9533333601
step 10: 10596666960
+ 06966669501
step 11: 17563336461
+ 16463336571
step 12: 34026673032
+ 23037662043
step 13: 57064335075
+ 57053346075
step 14: 114117681150
+ 051186711411
step 15: 165304392561
+ 165293403561
step 16: 330597796122
+ 221697795033
step 17: 552295591155
+ 551195592255
step 18: 1103491183410
+ 0143811943011
step 19: 1247303126421
+ 1246213037421
step 20: 2493516163842
+ 2483616153942
step 21: 4977132317784
+ 4877132317794
step 22: 9854264635578
+ 8755364624589
step 23: 18609629260167
+ 76106292690681
step 24: 94715921950848
+ 84805912951749
step 25: 179521834902597
+ 795209438125971
step 26: 974731273028568
+ 865820372137479
step 27: 1840551645166047
+ 7406615461550481
step 28: 9247167106716528
+ 8256176017617429
step 29: 17503343124333957
+ 75933342134330571
step 30: 93436685258664528
+ 82546685258663439
step 31: 175983370517327967
+ 769723715073389571
step 32: 945707085590717538
+ 835717095580707549
step 33: 1781424181171425087
+ 7805241711814241871
step 34: 9586665892985666958
+ 8596665892985666859
step 35: 18183331785971333817
+ 71833317958713338181
step 36: 90016649744684671998
+ 89917648644794661009
step 37: 179934298389479333007
+ 700333974983892439971
step 38: 880268273373371772978
+ 879277173373372862088
step 39: 1759545446746744635066
+ 6605364476476445459571
step 40: 8364909923223190094637
+ 7364900913223299094638
step 41: 15729810836446489189275
+ 57298198464463801892751
step 42: 73028009300910291082026
+ 62028019201900390082037
step 43: 135056028502810681164063
+ 360461186018205820650531
step 44: 495517214521016501814594
+ 495418105610125412715594
step 45: 990935320131141914530188
+ 881035419141131023539099
step 46: 1871970739272272938069287
+ 7829608392722729370791781
step 47: 9701579131995002308861068
+ 8601688032005991319751079
step 48: 18303267164000993628612147
+ 74121682639900046176230381
step 49: 92424949803901039804842528
+ 82524840893010930894942429
step 50: 174949790696911970699784957
+ 759487996079119696097949471
step 51: 934437786776031666797734428
+ 824437797666130677687734439
step 52: 1758875584442162344485468867
+ 7688645844432612444855788571
step 53: 9447521428874774789341257438
+ 8347521439874774788241257449
step 54: 17795042868749549577582514887
+ 78841528577594594786824059771
step 55: 96636571446344144364406574658
+ 85647560446344144364417563669
step 56: 182284131892688288728824138327
+ 723831428827882886298131482281
step 57: 906115560720571175026955620608
+ 806026559620571175027065511609
step 58: 1712142120341142350054021132217
+ 7122311204500532411430212412171
step 59: 8834453324841674761484233544388
178992 takes 59 iterations / steps to resolve into a 31 digit palindrome.

REVERSAL-ADDITION PALINDROME RECORDS

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 1,733,377 times since Saturday, March 9th, 2002.)