REVERSAL-ADDITION PALINDROME TEST ON 10309988

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 10309988:
10309988
+ 88990301
step 1: 99300289
+ 98200399
step 2: 197500688
+ 886005791
step 3: 1083506479
+ 9746053801
step 4: 10829560280
+ 08206592801
step 5: 19036153081
+ 18035163091
step 6: 37071316172
+ 27161317073
step 7: 64232633245
+ 54233623246
step 8: 118466256491
+ 194652664811
step 9: 313118921302
+ 203129811313
step 10: 516248732615
+ 516237842615
step 11: 1032486575230
+ 0325756842301
step 12: 1358243417531
+ 1357143428531
step 13: 2715386846062
+ 2606486835172
step 14: 5321873681234
+ 4321863781235
step 15: 9643737462469
+ 9642647373469
step 16: 19286384835938
+ 83953848368291
step 17: 103240233204229
+ 922402332042301
step 18: 1025642565246530
+ 0356425652465201
step 19: 1382068217711731
+ 1371177128602831
step 20: 2753245346314562
+ 2654136435423572
step 21: 5407381781738134
+ 4318371871837045
step 22: 9725753653575179
+ 9715753563575279
step 23: 19441507217150458
+ 85405171270514491
step 24: 104846678487664949
+ 949466784876648401
step 25: 1054313463364313350
+ 0533134633643134501
step 26: 1587448097007447851
+ 1587447007908447851
step 27: 3174895104915895702
+ 2075985194015984713
step 28: 5250880298931880415
+ 5140881398920880525
step 29: 10391761697852760940
+ 04906725879616719301
step 30: 15298487577469480241
+ 14208496477578489251
step 31: 29506984055047969492
+ 29496974055048960592
step 32: 59003958110096930084
+ 48003969001185930095
step 33: 107007927111282860179
+ 971068282111729700701
step 34: 1078076209223012560880
+ 0880652103229026708701
step 35: 1958728312452039269581
+ 1859629302542138278591
step 36: 3818357614994177548172
+ 2718457714994167538183
step 37: 6536815329988345086355
+ 5536805438899235186356
step 38: 12073620768887580272711
+ 11727208578886702637021
step 39: 23800829347774282909732
+ 23790928247774392800832
step 40: 47591757595548675710564
+ 46501757684559575719574
step 41: 94093515280108251430138
+ 83103415280108251539049
step 42: 177196930560216502969187
+ 781969205612065039691771
step 43: 959166136172281542660958
+ 859066245182271631661959
step 44: 1818232381354553174322917
+ 7192234713554531832328181
step 45: 9010467094909085006651098
+ 8901566005809094907640109
step 46: 17912033100718179914291207
+ 70219241997181700133021971
step 47: 88131275097899880047313178
+ 87131374008899879057213188
step 48: 175262649106799759104526366
+ 663625401957997601946262571
step 49: 838888051064797361050788937
+ 739887050163797460150888838
step 50: 1578775101228594821201677775
+ 5777761021284958221015778751
step 51: 7356536122513553042217456526
+ 6256547122403553152216356537
step 52: 13613083244917106194433813063
+ 36031833449160171944238031631
step 53: 49644916694077278138671844694
+ 49644817683187277049661944694
step 54: 99289734377264555188333789388
+ 88398733388155546277343798299
step 55: 187688467765420101465677587687
+ 786785776564101024567764886781
step 56: 974474244329521126033442474468
+ 864474244330621125923442474479
step 57: 1838948488660142251956884948947
+ 7498494886591522410668848498381
step 58: 9337443375251664662625733447328
+ 8237443375262664661525733447339
step 59: 17574886750514329324151466894667
+ 76649866415142392341505768847571
step 60: 94224753165656721665657235742238
+ 83224753275656612765656135742249
step 61: 177449506441313334431313371484487
+ 784484173313134433313144605944771
step 62: 961933679754447767744457977429258
+ 852924779754447767744457976339169
step 63: 1814858459508895535488915953768427
+ 7248673595198845355988059548584181
step 64: 9063532054707740891476975502352608
+ 8062532055796741980477074502353609
step 65: 17126064110504482871954050004706217
+ 71260740005045917828440501146062171
step 66: 88386804115550400700394551150768388
+ 88386705115549300700405551140868388
step 67: 176773509231099701400800102291636776
+ 677636192201008004107990132905377671
step 68: 854409701432107705508790235197014447
+ 744410791532097805507701234107904458
step 69: 1598820492964205511016491469304918905
+ 5098194039641946101155024692940288951
step 70: 6697014532606151612171516162245207856
+ 6587025422616151712161516062354107966
step 71: 13284039955222303324333032224599315822
+ 22851399542223033342330322255993048231
step 72: 36135439497445336666663354480592364053
+ 35046329508445336666663354479493453163
step 73: 71181769005890673333326708960085817216
+ 61271858006980762333337609850096718117
step 74: 132453627012871435666664318810182535333
+ 333535281018813466666534178210726354231
step 75: 465988908031684902333198497020908889564
+ 465988809020794891333209486130809889564
step 76: 931977717052479793666407983151718779128
+ 821977817151389704666397974250717779139
step 77: 1753955534203869498332805957402436558267
+ 7628556342047595082338949683024355593571
step 78: 9382511876251464580671755640426792151838
+ 8381512976240465571760854641526781152839
step 79: 17764024852491930152432610281953573304677
+ 77640337535918201623425103919425842046771
step 80: 95404362388410131775857714201379415351448
+ 84415351497310241775857713101488326340459
step 81: 179819713885720373551715427302867741691907
+ 709196147768203724517155373027588317918971
step 82: 889015861653924098068870800330456059610878
+ 878016950654033008078860890429356168510988
step 83: 1767032812307957106147731690759812228121866
+ 6681218222189570961377416017597032182307671
step 84: 8448251034497528067525147708356844410429537
+ 7359240144486538077415257608257944301528448
step 85: 15807491178984066144940405316614788711957985
+ 58975911788741661350404944166048987119470851
step 86: 74783402967725727495345349482663775831428836
+ 63882413857736628494354359472752776920438747
step 87: 138665816825462355989699708955416552751867583
+ 385768157255614559807996989553264528618566831
step 88: 524433974081076915797696698508681081370434414
+ 414434073180186805896696797519670180479334425
step 89: 938868047261263721694393496028351261849768839
+ 938867948162153820694393496127362162740868839
step 90: 1877735995423417542388786992155713424590637678
+ 8767360954243175512996878832457143245995377781
step 91: 10645096949666593055385665824612856670586015459
+ 95451068507665821642856658355039566694969054601
step 92: 106096165457332414698242324179652423365555070060
+ 060070555563324256971423242896414233754561690601
step 93: 166166721020656671669665567076066657120116760661
+ 166067611021756660670765566966176656020127661661
step 94: 332234332042413332340431134042243313140244422322
+ 223224442041313342240431134043233314240233432233
step 95: 555458774083726674580862268085476627380477854555
10309988 takes 95 iterations / steps to resolve into a 48 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 1,703,605 times since Saturday, March 9th, 2002.)