REVERSAL-ADDITION PALINDROME TEST ON 600579

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 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.

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 1,723,943 times since Saturday, March 9th, 2002.)