山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10000761554

    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 10000761554:
    10000761554
    + 45516700001
    step 1: 55517461555
    + 55516471555
    step 2: 111033933110
    + 011339330111
    step 3: 122373263221
    + 122362373221
    step 4: 244735636442
    + 244636537442
    step 5: 489372173884
    + 488371273984
    step 6: 977743447868
    + 868744347779
    step 7: 1846487795647
    + 7465977846481
    step 8: 9312465642128
    + 8212465642139
    step 9: 17524931284267
    + 76248213942571
    step 10: 93773145226838
    + 83862254137739
    step 11: 177635399364577
    + 775463993536771
    step 12: 953099392901348
    + 843109293990359
    step 13: 1796208686891707
    + 7071986868026971
    step 14: 8868195554918678
    + 8768194555918688
    step 15: 17636390110837366
    + 66373801109363671
    step 16: 84010191220201037
    + 73010202219101048
    step 17: 157020393439302085
    + 580203934393020751
    step 18: 737224327832322836
    + 638223238723422737
    step 19: 1375447566555745573
    + 3755475556657445731
    step 20: 5130923123213191304
    + 4031913123213290315
    step 21: 9162836246426481619
    + 9161846246426382619
    step 22: 18324682492852864238
    + 83246825829428642381
    step 23: 101571508322281506619
    + 916605182223805175101
    step 24: 1018176690546086681720
    + 0271866806450966718101
    step 25: 1290043496997053399821
    + 1289933507996943400921
    step 26: 2579977004993996800742
    + 2470086993994007799752
    step 27: 5050063998988004600494
    + 4940064008898993600505
    step 28: 9990128007886998200999
    + 9990028996887008210999
    step 29: 19980157004774006411998
    + 89911460047740075108991
    step 30: 109891617052514081520989
    + 989025180415250716198901
    step 31: 1098916797467764797719890
    + 0989177974677647976198901
    step 32: 2088094772145412773918791
    + 1978193772145412774908802
    step 33: 4066288544290825548827593
    + 3957288455280924458826604
    step 34: 8023576999571750007654197
    + 7914567000571759996753208
    step 35: 15938144000143510004407405
    + 50470440001534100044183951
    step 36: 66408584001677610048591356
    + 65319584001677610048580466
    step 37: 131728168003355220097171822
    + 228171790022553300861827131
    step 38: 359899958025908520958998953
    + 359899859025809520859998953
    step 39: 719799817051718041818997906
    + 609799818140817150718997917
    step 40: 1329599635192535192537995823
    + 3285997352915352915369959231
    step 41: 4615596988107888107907955054
    + 4505597097018887018896955164
    step 42: 9121194085126775126804910218
    + 8120194086215776215804911219
    step 43: 17241388171342551342609821437
    + 73412890624315524317188314271
    step 44: 90654278795658075659798135708
    + 80753189795657085659787245609
    step 45: 171407468591315161319585381317
    + 713183585913161513195864704171
    step 46: 884591054504476674515450085488
    + 884580054515476674405450195488
    step 47: 1769171109019953348920900280976
    + 6790820090298433599109011719671
    step 48: 8559991199318386948029912000647
    + 7460002199208496838139911999558
    step 49: 16019993398526883786169824000205
    + 50200042896168738862589339991061
    step 50: 66220036294695622648759163991266
    + 66219936195784622659649263002266
    step 51: 132439972490480245308408426993532
    + 235399624804803542084094279934231
    step 52: 367839597295283787392502706927763
    + 367729607205293787382592795938763
    step 53: 735569204500577574775095502866526
    + 625668205590577475775005402965537
    step 54: 1361237410091155050550100905832063
    + 3602385090010550505511900147321631
    step 55: 4963622500101705556062001053153694
    + 4963513501002606555071010052263694
    step 56: 9927136001104312111133011105417388
    + 8837145011103311112134011006317299
    step 57: 18764281012207623223267022111734687
    + 78643711122076232232670221018246781
    step 58: 97407992134283855455937243129981468
    + 86418992134273955455838243129970479
    step 59: 183826984268557810911775486259951947
    + 749159952684577119018755862489628381
    step 60: 932986936953134929930531348749580328
    + 823085947843135039929431359639689239
    step 61: 1756072884796269969859962708389269567
    + 7659629838072699589699626974882706571
    step 62: 9415702722868969559559589683271976138
    + 8316791723869859559559698682272075149
    step 63: 17732494446738829119119288365544051287
    + 78215044556388291191192883764449423771
    step 64: 95947539003127120310312172129993475058
    + 85057439992127121301302172130093574959
    step 65: 181004978995254241611614344260087050017
    + 710050780062443416116142452599879400181
    step 66: 891055759057697657727756796859966450198
    + 891054669958697657727756796750957550198
    step 67: 1782110429016395315455513593610924000396
    + 6930004290163953155545135936109240112871
    step 68: 8712114719180348471000649529720164113267
    + 7623114610279259460001748430819174112178
    step 69: 16335229329459607931002397960539338225445
    + 54452283393506979320013970695492392253361
    step 70: 70787512722966587251016368656031730478806
    + 60887403713065686361015278566922721578707
    step 71: 131674916436032273612031647222954452057513
    + 315750254459222746130216372230634619476131
    step 72: 447425170895255019742248019453589071533644
    + 446335170985354910842247910552598071524744
    step 73: 893760341880609930584495930006187143058388
    + 883850341781600039594485039906088143067398
    step 74: 1777610683662209970178980969912275286125786
    + 6875216825722199690898710799022663860167771
    step 75: 8652827509384409661077691768934939146293557
    + 7553926419394398671967701669044839057282568
    step 76: 16206753928778808333045393437979778203576125
    + 52167530287797973439354033380887782935760261
    step 77: 68374284216576781772399426818867561139336386
    + 68363393116576881862499327718767561248247386
    step 78: 136737677333153663634898754537635122387583772
    + 277385783221536735457898436366351333776737631
    step 79: 414123460554690399092797190903986456164321403
    + 304123461654689309091797290993096455064321414
    step 80: 718246922209379708184594481897082911228642817
    + 718246822119280798184495481807973902229642817
    step 81: 1436493744328660506369089963705056813458285634
    + 4365828543186505073699809636050668234473946341
    step 82: 5802322287515165580068899599755725047932231975
    + 5791322397405275579959988600855615157822232085
    step 83: 11593644684920441160028888200611340205754464060
    + 06046445750204311600288882006114402948644639511
    step 84: 17640090435124752760317770206725743154399103571
    + 17530199345134752760207771306725742153409004671
    step 85: 35170289780259505520525541513451485307808108242
    + 24280180870358415431514552502550595208798207153
    step 86: 59450470650617920952040094016002080516606315395
    + 59351360661508020061049004025902971605607405495
    step 87: 118801831312125941013089098041905052122213720890
    + 098027312221250509140890980310149521213138108811
    step 88: 216829143533376450153980078352054573335351829701
    + 107928153533375450253870089351054673335341928612
    step 89: 324757297066751900407850167703109246670693758313
    + 313857396076642901307761058704009157660792757423
    step 90: 638614693143394801715611226407118404331486515736
    + 637515684133404811704622116517108493341396416836
    step 91: 1276130377276799613420233342924226897672882932572
    + 2752392882767986224292433320243169976727730316721
    step 92: 4028523260044785837712666663167396874400613249293
    + 3929423160044786937613666662177385874400623258204
    step 93: 7957946420089572775326333325344782748801236507497
    + 7947056321088472874435233336235772759800246497597
    step 94: 15905002741178045649761566661580555508601483005094
    + 49050038410680555508516666516794654087114720050951
    step 95: 64955041151858601158278233178375209595716203056045
    + 54065030261759590257387133287285110685815114055946
    step 96: 119020071413618191415665366465660320281531317111991
    + 199111713135182023066564663566514191816314170020911
    step 97: 318131784548800214482230030032174512097845487132902
    + 209231784548790215471230030032284412008845487131813
    step 98: 527363569097590429953460060064458924106690974264715
    + 517462479096601429854460060064359924095790965363725
    step 99: 1044826048194191859807920120128818848202481939628440
    + 0448269391842028488188210210297089581914918406284401
    step 100: 1493095440036220347996130330425908430117400345912841
    + 1482195430047110348095240330316997430226300445903941
    step 101: 2975290870083330696091370660742905860343700791816782
    + 2876181970073430685092470660731906960333800780925792
    step 102: 5851472840156761381183841321474812820677501572742574
    + 4752472751057760282184741231483811831676510482741585
    step 103: 10603945591214521663368582552958624652354012055484159
    + 95148455021045325642685925528586336612541219554930601
    step 104: 105752400612259847306054508081544961264895231610414760
    + 067414016132598462169445180805450603748952216004257501
    step 105: 173166416744858309475499688886995565013847447614672261
    + 162276416744748310565599688886994574903858447614661371
    step 106: 335442833489606620041099377773990139917705895229333632
    + 236333922598507719931099377773990140026606984338244533
    step 107: 571776756088114339972198755547980279944312879567578165
    + 561875765978213449972089745557891279933411880657677175
    step 108: 1133652522066327789944288501105871559877724760225255340
    + 0435525220674277789551785011058824499877236602252563311
    step 109: 1569177742740605579496073512164696059754961362477818651
    + 1568187742631694579506964612153706949755060472477719651
    step 110: 3137365485372300159003038124318403009510021834955538302
    + 2038355594381200159003048134218303009510032735845637313
    step 111: 5175721079753500318006086258536706019020054570801175615
    + 5165711080754500209106076358526806008130053579701275715
    step 112: 10341432160508000527112162617063512027150108150502451330
    + 03315420505180105172021536071626121172500080506123414301
    step 113: 13656852665688105699133698688689633199650188656625865631
    10000761554 takes 113 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 2,061,837 times since Saturday, March 9th, 2002.)
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