REVERSAL-ADDITION PALINDROME TEST ON 190890

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 190890:
190890
+ 098091
step 1: 288981
+ 189882
step 2: 478863
+ 368874
step 3: 847737
+ 737748
step 4: 1585485
+ 5845851
step 5: 7431336
+ 6331347
step 6: 13762683
+ 38626731
step 7: 52389414
+ 41498325
step 8: 93887739
+ 93778839
step 9: 187666578
+ 875666781
step 10: 1063333359
+ 9533333601
step 11: 10596666960
+ 06966669501
step 12: 17563336461
+ 16463336571
step 13: 34026673032
+ 23037662043
step 14: 57064335075
+ 57053346075
step 15: 114117681150
+ 051186711411
step 16: 165304392561
+ 165293403561
step 17: 330597796122
+ 221697795033
step 18: 552295591155
+ 551195592255
step 19: 1103491183410
+ 0143811943011
step 20: 1247303126421
+ 1246213037421
step 21: 2493516163842
+ 2483616153942
step 22: 4977132317784
+ 4877132317794
step 23: 9854264635578
+ 8755364624589
step 24: 18609629260167
+ 76106292690681
step 25: 94715921950848
+ 84805912951749
step 26: 179521834902597
+ 795209438125971
step 27: 974731273028568
+ 865820372137479
step 28: 1840551645166047
+ 7406615461550481
step 29: 9247167106716528
+ 8256176017617429
step 30: 17503343124333957
+ 75933342134330571
step 31: 93436685258664528
+ 82546685258663439
step 32: 175983370517327967
+ 769723715073389571
step 33: 945707085590717538
+ 835717095580707549
step 34: 1781424181171425087
+ 7805241711814241871
step 35: 9586665892985666958
+ 8596665892985666859
step 36: 18183331785971333817
+ 71833317958713338181
step 37: 90016649744684671998
+ 89917648644794661009
step 38: 179934298389479333007
+ 700333974983892439971
step 39: 880268273373371772978
+ 879277173373372862088
step 40: 1759545446746744635066
+ 6605364476476445459571
step 41: 8364909923223190094637
+ 7364900913223299094638
step 42: 15729810836446489189275
+ 57298198464463801892751
step 43: 73028009300910291082026
+ 62028019201900390082037
step 44: 135056028502810681164063
+ 360461186018205820650531
step 45: 495517214521016501814594
+ 495418105610125412715594
step 46: 990935320131141914530188
+ 881035419141131023539099
step 47: 1871970739272272938069287
+ 7829608392722729370791781
step 48: 9701579131995002308861068
+ 8601688032005991319751079
step 49: 18303267164000993628612147
+ 74121682639900046176230381
step 50: 92424949803901039804842528
+ 82524840893010930894942429
step 51: 174949790696911970699784957
+ 759487996079119696097949471
step 52: 934437786776031666797734428
+ 824437797666130677687734439
step 53: 1758875584442162344485468867
+ 7688645844432612444855788571
step 54: 9447521428874774789341257438
+ 8347521439874774788241257449
step 55: 17795042868749549577582514887
+ 78841528577594594786824059771
step 56: 96636571446344144364406574658
+ 85647560446344144364417563669
step 57: 182284131892688288728824138327
+ 723831428827882886298131482281
step 58: 906115560720571175026955620608
+ 806026559620571175027065511609
step 59: 1712142120341142350054021132217
+ 7122311204500532411430212412171
step 60: 8834453324841674761484233544388
190890 takes 60 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 1,750,297 times since Saturday, March 9th, 2002.)