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                    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 2,095,958 times since Saturday, March 9th, 2002.)

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