REVERSAL-ADDITION PALINDROME TEST ON 10000442119

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 10000442119:
10000442119
+ 91124400001
step 1: 101124842120
+ 021248421101
step 2: 122373263221
+ 122362373221
step 3: 244735636442
+ 244636537442
step 4: 489372173884
+ 488371273984
step 5: 977743447868
+ 868744347779
step 6: 1846487795647
+ 7465977846481
step 7: 9312465642128
+ 8212465642139
step 8: 17524931284267
+ 76248213942571
step 9: 93773145226838
+ 83862254137739
step 10: 177635399364577
+ 775463993536771
step 11: 953099392901348
+ 843109293990359
step 12: 1796208686891707
+ 7071986868026971
step 13: 8868195554918678
+ 8768194555918688
step 14: 17636390110837366
+ 66373801109363671
step 15: 84010191220201037
+ 73010202219101048
step 16: 157020393439302085
+ 580203934393020751
step 17: 737224327832322836
+ 638223238723422737
step 18: 1375447566555745573
+ 3755475556657445731
step 19: 5130923123213191304
+ 4031913123213290315
step 20: 9162836246426481619
+ 9161846246426382619
step 21: 18324682492852864238
+ 83246825829428642381
step 22: 101571508322281506619
+ 916605182223805175101
step 23: 1018176690546086681720
+ 0271866806450966718101
step 24: 1290043496997053399821
+ 1289933507996943400921
step 25: 2579977004993996800742
+ 2470086993994007799752
step 26: 5050063998988004600494
+ 4940064008898993600505
step 27: 9990128007886998200999
+ 9990028996887008210999
step 28: 19980157004774006411998
+ 89911460047740075108991
step 29: 109891617052514081520989
+ 989025180415250716198901
step 30: 1098916797467764797719890
+ 0989177974677647976198901
step 31: 2088094772145412773918791
+ 1978193772145412774908802
step 32: 4066288544290825548827593
+ 3957288455280924458826604
step 33: 8023576999571750007654197
+ 7914567000571759996753208
step 34: 15938144000143510004407405
+ 50470440001534100044183951
step 35: 66408584001677610048591356
+ 65319584001677610048580466
step 36: 131728168003355220097171822
+ 228171790022553300861827131
step 37: 359899958025908520958998953
+ 359899859025809520859998953
step 38: 719799817051718041818997906
+ 609799818140817150718997917
step 39: 1329599635192535192537995823
+ 3285997352915352915369959231
step 40: 4615596988107888107907955054
+ 4505597097018887018896955164
step 41: 9121194085126775126804910218
+ 8120194086215776215804911219
step 42: 17241388171342551342609821437
+ 73412890624315524317188314271
step 43: 90654278795658075659798135708
+ 80753189795657085659787245609
step 44: 171407468591315161319585381317
+ 713183585913161513195864704171
step 45: 884591054504476674515450085488
+ 884580054515476674405450195488
step 46: 1769171109019953348920900280976
+ 6790820090298433599109011719671
step 47: 8559991199318386948029912000647
+ 7460002199208496838139911999558
step 48: 16019993398526883786169824000205
+ 50200042896168738862589339991061
step 49: 66220036294695622648759163991266
+ 66219936195784622659649263002266
step 50: 132439972490480245308408426993532
+ 235399624804803542084094279934231
step 51: 367839597295283787392502706927763
+ 367729607205293787382592795938763
step 52: 735569204500577574775095502866526
+ 625668205590577475775005402965537
step 53: 1361237410091155050550100905832063
+ 3602385090010550505511900147321631
step 54: 4963622500101705556062001053153694
+ 4963513501002606555071010052263694
step 55: 9927136001104312111133011105417388
+ 8837145011103311112134011006317299
step 56: 18764281012207623223267022111734687
+ 78643711122076232232670221018246781
step 57: 97407992134283855455937243129981468
+ 86418992134273955455838243129970479
step 58: 183826984268557810911775486259951947
+ 749159952684577119018755862489628381
step 59: 932986936953134929930531348749580328
+ 823085947843135039929431359639689239
step 60: 1756072884796269969859962708389269567
+ 7659629838072699589699626974882706571
step 61: 9415702722868969559559589683271976138
+ 8316791723869859559559698682272075149
step 62: 17732494446738829119119288365544051287
+ 78215044556388291191192883764449423771
step 63: 95947539003127120310312172129993475058
+ 85057439992127121301302172130093574959
step 64: 181004978995254241611614344260087050017
+ 710050780062443416116142452599879400181
step 65: 891055759057697657727756796859966450198
+ 891054669958697657727756796750957550198
step 66: 1782110429016395315455513593610924000396
+ 6930004290163953155545135936109240112871
step 67: 8712114719180348471000649529720164113267
+ 7623114610279259460001748430819174112178
step 68: 16335229329459607931002397960539338225445
+ 54452283393506979320013970695492392253361
step 69: 70787512722966587251016368656031730478806
+ 60887403713065686361015278566922721578707
step 70: 131674916436032273612031647222954452057513
+ 315750254459222746130216372230634619476131
step 71: 447425170895255019742248019453589071533644
+ 446335170985354910842247910552598071524744
step 72: 893760341880609930584495930006187143058388
+ 883850341781600039594485039906088143067398
step 73: 1777610683662209970178980969912275286125786
+ 6875216825722199690898710799022663860167771
step 74: 8652827509384409661077691768934939146293557
+ 7553926419394398671967701669044839057282568
step 75: 16206753928778808333045393437979778203576125
+ 52167530287797973439354033380887782935760261
step 76: 68374284216576781772399426818867561139336386
+ 68363393116576881862499327718767561248247386
step 77: 136737677333153663634898754537635122387583772
+ 277385783221536735457898436366351333776737631
step 78: 414123460554690399092797190903986456164321403
+ 304123461654689309091797290993096455064321414
step 79: 718246922209379708184594481897082911228642817
+ 718246822119280798184495481807973902229642817
step 80: 1436493744328660506369089963705056813458285634
+ 4365828543186505073699809636050668234473946341
step 81: 5802322287515165580068899599755725047932231975
+ 5791322397405275579959988600855615157822232085
step 82: 11593644684920441160028888200611340205754464060
+ 06046445750204311600288882006114402948644639511
step 83: 17640090435124752760317770206725743154399103571
+ 17530199345134752760207771306725742153409004671
step 84: 35170289780259505520525541513451485307808108242
+ 24280180870358415431514552502550595208798207153
step 85: 59450470650617920952040094016002080516606315395
+ 59351360661508020061049004025902971605607405495
step 86: 118801831312125941013089098041905052122213720890
+ 098027312221250509140890980310149521213138108811
step 87: 216829143533376450153980078352054573335351829701
+ 107928153533375450253870089351054673335341928612
step 88: 324757297066751900407850167703109246670693758313
+ 313857396076642901307761058704009157660792757423
step 89: 638614693143394801715611226407118404331486515736
+ 637515684133404811704622116517108493341396416836
step 90: 1276130377276799613420233342924226897672882932572
+ 2752392882767986224292433320243169976727730316721
step 91: 4028523260044785837712666663167396874400613249293
+ 3929423160044786937613666662177385874400623258204
step 92: 7957946420089572775326333325344782748801236507497
+ 7947056321088472874435233336235772759800246497597
step 93: 15905002741178045649761566661580555508601483005094
+ 49050038410680555508516666516794654087114720050951
step 94: 64955041151858601158278233178375209595716203056045
+ 54065030261759590257387133287285110685815114055946
step 95: 119020071413618191415665366465660320281531317111991
+ 199111713135182023066564663566514191816314170020911
step 96: 318131784548800214482230030032174512097845487132902
+ 209231784548790215471230030032284412008845487131813
step 97: 527363569097590429953460060064458924106690974264715
+ 517462479096601429854460060064359924095790965363725
step 98: 1044826048194191859807920120128818848202481939628440
+ 0448269391842028488188210210297089581914918406284401
step 99: 1493095440036220347996130330425908430117400345912841
+ 1482195430047110348095240330316997430226300445903941
step 100: 2975290870083330696091370660742905860343700791816782
+ 2876181970073430685092470660731906960333800780925792
step 101: 5851472840156761381183841321474812820677501572742574
+ 4752472751057760282184741231483811831676510482741585
step 102: 10603945591214521663368582552958624652354012055484159
+ 95148455021045325642685925528586336612541219554930601
step 103: 105752400612259847306054508081544961264895231610414760
+ 067414016132598462169445180805450603748952216004257501
step 104: 173166416744858309475499688886995565013847447614672261
+ 162276416744748310565599688886994574903858447614661371
step 105: 335442833489606620041099377773990139917705895229333632
+ 236333922598507719931099377773990140026606984338244533
step 106: 571776756088114339972198755547980279944312879567578165
+ 561875765978213449972089745557891279933411880657677175
step 107: 1133652522066327789944288501105871559877724760225255340
+ 0435525220674277789551785011058824499877236602252563311
step 108: 1569177742740605579496073512164696059754961362477818651
+ 1568187742631694579506964612153706949755060472477719651
step 109: 3137365485372300159003038124318403009510021834955538302
+ 2038355594381200159003048134218303009510032735845637313
step 110: 5175721079753500318006086258536706019020054570801175615
+ 5165711080754500209106076358526806008130053579701275715
step 111: 10341432160508000527112162617063512027150108150502451330
+ 03315420505180105172021536071626121172500080506123414301
step 112: 13656852665688105699133698688689633199650188656625865631
10000442119 takes 112 iterations / steps to resolve into a 56 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 1,704,972 times since Saturday, March 9th, 2002.)