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                    REVERSAL-ADDITION PALINDROME TEST ON 100000055859

                    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 100000055859:
                    100000055859
                    + 958550000001
                    step 1: 1058550055860
                    + 0685500558501
                    step 2: 1744050614361
                    + 1634160504471
                    step 3: 3378211118832
                    + 2388111128733
                    step 4: 5766322247565
                    + 5657422236675
                    step 5: 11423744484240
                    + 04248444732411
                    step 6: 15672189216651
                    + 15661298127651
                    step 7: 31333487344302
                    + 20344378433313
                    step 8: 51677865777615
                    + 51677756877615
                    step 9: 103355622655230
                    + 032556226553301
                    step 10: 135911849208531
                    + 135802948119531
                    step 11: 271714797328062
                    + 260823797417172
                    step 12: 532538594745234
                    + 432547495835235
                    step 13: 965086090580469
                    + 964085090680569
                    step 14: 1929171181261038
                    + 8301621811719291
                    step 15: 10230792992980329
                    + 92308929929703201
                    step 16: 102539722922683530
                    + 035386229227935201
                    step 17: 137925952150618731
                    + 137816051259529731
                    step 18: 275742003410148462
                    + 264841014300247572
                    step 19: 540583017710396034
                    + 430693017710385045
                    step 20: 971276035420781079
                    + 970187024530672179
                    step 21: 1941463059951453258
                    + 8523541599503641491
                    step 22: 10465004659455094749
                    + 94749055495640056401
                    step 23: 105214060155095151150
                    + 051151590551060412501
                    step 24: 156365650706155563651
                    + 156365551607056563651
                    step 25: 312731202313212127302
                    + 203721212313202137213
                    step 26: 516452414626414264515
                    + 515462414626414254615
                    step 27: 1031914829252828519130
                    + 0319158282529284191301
                    step 28: 1351073111782112710431
                    + 1340172112871113701531
                    step 29: 2691245224653226411962
                    + 2691146223564225421962
                    step 30: 5382391448217451833924
                    + 4293381547128441932835
                    step 31: 9675772995345893766759
                    + 9576673985435992775769
                    step 32: 19252446980781886542528
                    + 82524568818708964425291
                    step 33: 101777015799490850967819
                    + 918769058094997510777101
                    step 34: 1020546073894488361744920
                    + 0294471638844983706450201
                    step 35: 1315017712739472068195121
                    + 1215918602749372177105131
                    step 36: 2530936315488844245300252
                    + 2520035424488845136390352
                    step 37: 5050971739977689381690604
                    + 4060961839867799371790505
                    step 38: 9111933579845488753481109
                    + 9011843578845489753391119
                    step 39: 18123777158690978506872228
                    + 82227860587909685177732181
                    step 40: 100351637746600663684604409
                    + 904406486366006647736153001
                    step 41: 1004758124112607311420757410
                    + 0147570241137062114218574001
                    step 42: 1152328365249669425639331411
                    + 1141339365249669425638232511
                    step 43: 2293667730499338851277563922
                    + 2293657721588339940377663922
                    step 44: 4587325452087678791655227844
                    + 4487225561978767802545237854
                    step 45: 9074551014066446594200465698
                    + 8965640024956446604101554709
                    step 46: 18040191039022893198302020407
                    + 70402020389139822093019104081
                    step 47: 88442211428162715291321124488
                    + 88442112319251726182411224488
                    step 48: 176884323747414441473732348976
                    + 679843237374144414747323488671
                    step 49: 856727561121558856221055837647
                    + 746738550122658855121165727658
                    step 50: 1603466111244217711342221565305
                    + 5035651222431177124421116643061
                    step 51: 6639117333675394835763338208366
                    + 6638028333675384935763337119366
                    step 52: 13277145667350779771526675327732
                    + 23772357662517797705376654177231
                    step 53: 37049503329868577476903329504963
                    + 36940592330967477586892330594073
                    step 54: 73990095660836055063795660099036
                    + 63099006659736055063806659009937
                    step 55: 137089102320572110127602319108973
                    + 379801913206721011275023201980731
                    step 56: 516891015527293121402625521089704
                    + 407980125526204121392725510198615
                    step 57: 924871141053497242795351031288319
                    + 913882130153597242794350141178429
                    step 58: 1838753271207094485589701172466748
                    + 8476642711079855844907021723578381
                    step 59: 10315395982286950330496722896045129
                    + 92154069822769403305968228959351301
                    step 60: 102469465805056353636464951855396430
                    + 034693558159464636353650508564964201
                    step 61: 137163023964520989990115460420360631
                    + 136063024064511099989025469320361731
                    step 62: 273226048029032089979140929740722362
                    + 263227047929041979980230920840622372
                    step 63: 536453095958074069959371850581344734
                    + 437443185058173959960470859590354635
                    step 64: 973896281016248029919842710171699369
                    + 963996171017248919920842610182698379
                    step 65: 1937892452033496949840685320354397748
                    + 8477934530235860489496943302542987391
                    step 66: 10415826982269357439337628622897385139
                    + 93158379822682673393475396228962851401
                    step 67: 103574206804952030832813024851860236540
                    + 045632068158420318238030259408602475301
                    step 68: 149206274963372349070843284260462711841
                    + 148117264062482348070943273369472602941
                    step 69: 297323539025854697141786557629935314782
                    + 287413539926755687141796458520935323792
                    step 70: 584737078952610384283583016150870638574
                    + 475836078051610385382483016259870737485
                    step 71: 1060573157004220769666066032410741376059
                    + 9506731470142306606669670224007513750601
                    step 72: 10567304627146527376335736256418255126660
                    + 06662155281465263753367372564172640376501
                    step 73: 17229459908611791129703108820590895503161
                    + 16130559809502880130792119711680995492271
                    step 74: 33360019718114671260495228532271890995432
                    + 23459909817223582259406217641181791006333
                    step 75: 56819929535338253519901446173453682001765
                    + 56710028635437164410991535283353592991865
                    step 76: 113529958170775417930892981456807274993630
                    + 036399472708654189298039714577071859925311
                    step 77: 149929430879429607228932696033879134918941
                    + 149819431978330696239822706924978034929941
                    step 78: 299748862857760303468755402958857169848882
                    + 288848961758859204557864303067758268847992
                    step 79: 588597824616619508026619706026615438696874
                    + 478696834516620607916620805916616428795885
                    step 80: 1067294659133240115943240511943231867492759
                    + 9572947681323491150423495110423319564927601
                    step 81: 10640242340456731266366735622366551432420360
                    + 06302423415566322653766366213765404324204601
                    step 82: 16942665756023053920133101836131955756624961
                    + 16942665755913163810133102935032065756624961
                    step 83: 33885331511936217730266204771164021513249922
                    + 22994231512046117740266203771263911513358833
                    step 84: 56879563023982335470532408542427933026608755
                    + 55780662033972424580423507453328932036597865
                    step 85: 112660225057954760050955915995756865063206620
                    + 026602360568657599519559050067459750522066211
                    step 86: 139262585626612359570514966063216615585272831
                    + 138272585516612360669415075953216626585262931
                    step 87: 277535171143224720239930042016433242170535762
                    + 267535071242334610240039932027422341171535772
                    step 88: 545070242385559330479969974043855583342071534
                    + 435170243385558340479969974033955583242070545
                    step 89: 980240485771117670959939948077811166584142079
                    + 970241485661118770849939959076711177584042089
                    step 90: 1950481971432236441809879907154522344168184168
                    + 8614818614432254517099789081446322341791840591
                    step 91: 10565300585864490958909668988600844685960024759
                    + 95742006958644800688986690985909446858500356501
                    step 92: 106307307544509291647896359974510291544460381260
                    + 062183064445192015479953698746192905445703703601
                    step 93: 168490371989701307127850058720703196990164084861
                    + 168480461099691307027850058721703107989173094861
                    step 94: 336970833089392614155700117442406304979337179722
                    + 227971733979403604244711007551416293980338079633
                    step 95: 564942567068796218400411124993822598959675259355
                    + 553952576959895228399421114004812697860765249465
                    step 96: 1118895144028691446799832238998635296820440508820
                    + 0288050440286925368998322389976441968204415988111
                    step 97: 1406945584315616815798154628975077265024856496931
                    + 1396946584205627705798264518975186165134855496041
                    step 98: 2803892168521244521596419147950263430159711992972
                    + 2792991179510343620597419146951254421258612983082
                    step 99: 5596883348031588142193838294901517851418324976054
                    + 4506794238141587151094928383912418851308433886955
                    step 100: 10103677586173175293288766678813936702726758863009
                    + 90036885762720763931887666788239257137168577630101
                    step 101: 100140563348893939225176433467053193839895336493110
                    + 011394633598938391350764334671522939398843365041001
                    step 102: 111535196947832330575940768138576133238738701534111
                    + 111435107837832331675831867049575033238749691535111
                    step 103: 222970304785664662251772635188151166477488393069222
                    + 222960393884774661151881536277152266466587403079222
                    step 104: 445930698670439323403654171465303432944075796148444
                    + 444841697570449234303564171456304323934076896039544
                    step 105: 890772396240888557707218342921607756878152692187988
                    + 889781296251878657706129243812707755888042693277098
                    step 106: 1780553692492767215413347586734315512766195385465086
                    + 6805645835916672155134376857433145127672942963550871
                    step 107: 8586199528409439370547724444167460640439138349015957
                    + 7595109438319340460647614444277450739349048259916858
                    step 108: 16181308966728779831195338888444911379788186608932815
                    + 51823980668188797311944488883359113897782766980318161
                    step 109: 68005289634917577143139827771804025277570953589250976
                    + 67905298535907577252040817772893134177571943698250086
                    step 110: 135910588170825154395180645544697159455142897287501062
                    + 260105782798241554951796445546081593451528071885019531
                    step 111: 396016370969066709346977091090778752906670969172520593
                    + 395025271969076609257877090190779643907660969073610693
                    step 112: 791041642938143318604854181281558396814331938246131286
                    + 682131642839133418693855182181458406813341839246140197
                    step 113: 1473173285777276737298709363463016803627673777492271483
                    + 3841722947773767263086103643639078927376727775823713741
                    step 114: 5314896233551044000384813007102095731004401553315985224
                    + 4225895133551044001375902017003184830004401553326984135
                    step 115: 9540791367102088001760715024105280561008803106642969359
                    + 9539692466013088001650825014205170671008802017631970459
                    step 116: 19080483833115176003411540038310451232017605124274939818
                    + 81893947242150671023215401383004511430067151133838408091
                    step 117: 100974431075265847026626941421314962662084756258113347909
                    + 909743311852657480266269413124149626620748562570134479001
                    step 118: 1010717742927923327292896354545464589282833318828247826910
                    + 0196287428288133382829854645454536982927233297292477170101
                    step 119: 1207005171216056710122751000000001572210066616120724997011
                    + 1107994270216166600122751000000001572210176506121715007021
                    step 120: 2314999441432223310245502000000003144420243122242440004032
                    + 2304000442422213420244413000000002055420133222341449994132
                    step 121: 4618999883854436730489915000000005199840376344583889998164
                    100000055859 takes 121 iterations / steps to resolve into a 58 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 2,095,706 times since Saturday, March 9th, 2002.)

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