REVERSAL-ADDITION PALINDROME TEST ON 10006198250

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 10006198250:
10006198250
+ 05289160001
step 1: 15295358251
+ 15285359251
step 2: 30580717502
+ 20571708503
step 3: 51152426005
+ 50062425115
step 4: 101214851120
+ 021158412101
step 5: 122373263221
+ 122362373221
step 6: 244735636442
+ 244636537442
step 7: 489372173884
+ 488371273984
step 8: 977743447868
+ 868744347779
step 9: 1846487795647
+ 7465977846481
step 10: 9312465642128
+ 8212465642139
step 11: 17524931284267
+ 76248213942571
step 12: 93773145226838
+ 83862254137739
step 13: 177635399364577
+ 775463993536771
step 14: 953099392901348
+ 843109293990359
step 15: 1796208686891707
+ 7071986868026971
step 16: 8868195554918678
+ 8768194555918688
step 17: 17636390110837366
+ 66373801109363671
step 18: 84010191220201037
+ 73010202219101048
step 19: 157020393439302085
+ 580203934393020751
step 20: 737224327832322836
+ 638223238723422737
step 21: 1375447566555745573
+ 3755475556657445731
step 22: 5130923123213191304
+ 4031913123213290315
step 23: 9162836246426481619
+ 9161846246426382619
step 24: 18324682492852864238
+ 83246825829428642381
step 25: 101571508322281506619
+ 916605182223805175101
step 26: 1018176690546086681720
+ 0271866806450966718101
step 27: 1290043496997053399821
+ 1289933507996943400921
step 28: 2579977004993996800742
+ 2470086993994007799752
step 29: 5050063998988004600494
+ 4940064008898993600505
step 30: 9990128007886998200999
+ 9990028996887008210999
step 31: 19980157004774006411998
+ 89911460047740075108991
step 32: 109891617052514081520989
+ 989025180415250716198901
step 33: 1098916797467764797719890
+ 0989177974677647976198901
step 34: 2088094772145412773918791
+ 1978193772145412774908802
step 35: 4066288544290825548827593
+ 3957288455280924458826604
step 36: 8023576999571750007654197
+ 7914567000571759996753208
step 37: 15938144000143510004407405
+ 50470440001534100044183951
step 38: 66408584001677610048591356
+ 65319584001677610048580466
step 39: 131728168003355220097171822
+ 228171790022553300861827131
step 40: 359899958025908520958998953
+ 359899859025809520859998953
step 41: 719799817051718041818997906
+ 609799818140817150718997917
step 42: 1329599635192535192537995823
+ 3285997352915352915369959231
step 43: 4615596988107888107907955054
+ 4505597097018887018896955164
step 44: 9121194085126775126804910218
+ 8120194086215776215804911219
step 45: 17241388171342551342609821437
+ 73412890624315524317188314271
step 46: 90654278795658075659798135708
+ 80753189795657085659787245609
step 47: 171407468591315161319585381317
+ 713183585913161513195864704171
step 48: 884591054504476674515450085488
+ 884580054515476674405450195488
step 49: 1769171109019953348920900280976
+ 6790820090298433599109011719671
step 50: 8559991199318386948029912000647
+ 7460002199208496838139911999558
step 51: 16019993398526883786169824000205
+ 50200042896168738862589339991061
step 52: 66220036294695622648759163991266
+ 66219936195784622659649263002266
step 53: 132439972490480245308408426993532
+ 235399624804803542084094279934231
step 54: 367839597295283787392502706927763
+ 367729607205293787382592795938763
step 55: 735569204500577574775095502866526
+ 625668205590577475775005402965537
step 56: 1361237410091155050550100905832063
+ 3602385090010550505511900147321631
step 57: 4963622500101705556062001053153694
+ 4963513501002606555071010052263694
step 58: 9927136001104312111133011105417388
+ 8837145011103311112134011006317299
step 59: 18764281012207623223267022111734687
+ 78643711122076232232670221018246781
step 60: 97407992134283855455937243129981468
+ 86418992134273955455838243129970479
step 61: 183826984268557810911775486259951947
+ 749159952684577119018755862489628381
step 62: 932986936953134929930531348749580328
+ 823085947843135039929431359639689239
step 63: 1756072884796269969859962708389269567
+ 7659629838072699589699626974882706571
step 64: 9415702722868969559559589683271976138
+ 8316791723869859559559698682272075149
step 65: 17732494446738829119119288365544051287
+ 78215044556388291191192883764449423771
step 66: 95947539003127120310312172129993475058
+ 85057439992127121301302172130093574959
step 67: 181004978995254241611614344260087050017
+ 710050780062443416116142452599879400181
step 68: 891055759057697657727756796859966450198
+ 891054669958697657727756796750957550198
step 69: 1782110429016395315455513593610924000396
+ 6930004290163953155545135936109240112871
step 70: 8712114719180348471000649529720164113267
+ 7623114610279259460001748430819174112178
step 71: 16335229329459607931002397960539338225445
+ 54452283393506979320013970695492392253361
step 72: 70787512722966587251016368656031730478806
+ 60887403713065686361015278566922721578707
step 73: 131674916436032273612031647222954452057513
+ 315750254459222746130216372230634619476131
step 74: 447425170895255019742248019453589071533644
+ 446335170985354910842247910552598071524744
step 75: 893760341880609930584495930006187143058388
+ 883850341781600039594485039906088143067398
step 76: 1777610683662209970178980969912275286125786
+ 6875216825722199690898710799022663860167771
step 77: 8652827509384409661077691768934939146293557
+ 7553926419394398671967701669044839057282568
step 78: 16206753928778808333045393437979778203576125
+ 52167530287797973439354033380887782935760261
step 79: 68374284216576781772399426818867561139336386
+ 68363393116576881862499327718767561248247386
step 80: 136737677333153663634898754537635122387583772
+ 277385783221536735457898436366351333776737631
step 81: 414123460554690399092797190903986456164321403
+ 304123461654689309091797290993096455064321414
step 82: 718246922209379708184594481897082911228642817
+ 718246822119280798184495481807973902229642817
step 83: 1436493744328660506369089963705056813458285634
+ 4365828543186505073699809636050668234473946341
step 84: 5802322287515165580068899599755725047932231975
+ 5791322397405275579959988600855615157822232085
step 85: 11593644684920441160028888200611340205754464060
+ 06046445750204311600288882006114402948644639511
step 86: 17640090435124752760317770206725743154399103571
+ 17530199345134752760207771306725742153409004671
step 87: 35170289780259505520525541513451485307808108242
+ 24280180870358415431514552502550595208798207153
step 88: 59450470650617920952040094016002080516606315395
+ 59351360661508020061049004025902971605607405495
step 89: 118801831312125941013089098041905052122213720890
+ 098027312221250509140890980310149521213138108811
step 90: 216829143533376450153980078352054573335351829701
+ 107928153533375450253870089351054673335341928612
step 91: 324757297066751900407850167703109246670693758313
+ 313857396076642901307761058704009157660792757423
step 92: 638614693143394801715611226407118404331486515736
+ 637515684133404811704622116517108493341396416836
step 93: 1276130377276799613420233342924226897672882932572
+ 2752392882767986224292433320243169976727730316721
step 94: 4028523260044785837712666663167396874400613249293
+ 3929423160044786937613666662177385874400623258204
step 95: 7957946420089572775326333325344782748801236507497
+ 7947056321088472874435233336235772759800246497597
step 96: 15905002741178045649761566661580555508601483005094
+ 49050038410680555508516666516794654087114720050951
step 97: 64955041151858601158278233178375209595716203056045
+ 54065030261759590257387133287285110685815114055946
step 98: 119020071413618191415665366465660320281531317111991
+ 199111713135182023066564663566514191816314170020911
step 99: 318131784548800214482230030032174512097845487132902
+ 209231784548790215471230030032284412008845487131813
step 100: 527363569097590429953460060064458924106690974264715
+ 517462479096601429854460060064359924095790965363725
step 101: 1044826048194191859807920120128818848202481939628440
+ 0448269391842028488188210210297089581914918406284401
step 102: 1493095440036220347996130330425908430117400345912841
+ 1482195430047110348095240330316997430226300445903941
step 103: 2975290870083330696091370660742905860343700791816782
+ 2876181970073430685092470660731906960333800780925792
step 104: 5851472840156761381183841321474812820677501572742574
+ 4752472751057760282184741231483811831676510482741585
step 105: 10603945591214521663368582552958624652354012055484159
+ 95148455021045325642685925528586336612541219554930601
step 106: 105752400612259847306054508081544961264895231610414760
+ 067414016132598462169445180805450603748952216004257501
step 107: 173166416744858309475499688886995565013847447614672261
+ 162276416744748310565599688886994574903858447614661371
step 108: 335442833489606620041099377773990139917705895229333632
+ 236333922598507719931099377773990140026606984338244533
step 109: 571776756088114339972198755547980279944312879567578165
+ 561875765978213449972089745557891279933411880657677175
step 110: 1133652522066327789944288501105871559877724760225255340
+ 0435525220674277789551785011058824499877236602252563311
step 111: 1569177742740605579496073512164696059754961362477818651
+ 1568187742631694579506964612153706949755060472477719651
step 112: 3137365485372300159003038124318403009510021834955538302
+ 2038355594381200159003048134218303009510032735845637313
step 113: 5175721079753500318006086258536706019020054570801175615
+ 5165711080754500209106076358526806008130053579701275715
step 114: 10341432160508000527112162617063512027150108150502451330
+ 03315420505180105172021536071626121172500080506123414301
step 115: 13656852665688105699133698688689633199650188656625865631
10006198250 takes 115 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 1,716,099 times since Saturday, March 9th, 2002.)