REVERSAL-ADDITION
PALINDROME
TEST ON
100000109584608
|
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 100000109584608: |
100000109584608
+ 806485901000001
step 1: 906486010584609
+ 906485010684609
step 2: 1812971021269218
+ 8129621201792181
step 3: 9942592223061399
+ 9931603222952499
step 4: 19874195446013898
+ 89831064459147891
step 5: 109705259905161789
+ 987161509952507901
step 6: 1096866769857669690
+ 0969667589676686901
step 7: 2066534359534356591
+ 1956534359534356602
step 8: 4023068719068713193
+ 3913178609178603204
step 9: 7936247328247316397
+ 7936137428237426397
step 10: 15872384756484742794
+ 49724748465748327851
step 11: 65597133222233070645
+ 54607033222233179556
step 12: 120204166444466250201
+ 102052664444661402021
step 13: 222256830889127652222
+ 222256721988038652222
step 14: 444513552877166304444
+ 444403661778255315444
step 15: 888917214655421619888
+ 888916124556412719888
step 16: 1777833339211834339776
+ 6779334381129333387771
step 17: 8557167720341167727547
+ 7457277611430277617558
step 18: 16014445331771445345105
+ 50154354417713354441061
step 19: 66168799749484799786166
+ 66168799748494799786166
step 20: 132337599497979599572332
+ 233275995979794995733231
step 21: 365613595477774595305563
+ 365503595477774595316563
step 22: 731117190955549190622126
+ 621226091945559091711137
step 23: 1352343282901108282333263
+ 3623332828011092823432531
step 24: 4975676110912201105765794
+ 4975675011022190116765794
step 25: 9951351121934391222531588
+ 8851352221934391211531599
step 26: 18802703343868782434063187
+ 78136043428786834330720881
step 27: 96938746772655616764784068
+ 86048746761655627764783969
step 28: 182987493534311244529568037
+ 730865925442113435394789281
step 29: 913853418976424679924357318
+ 813753429976424679814358319
step 30: 1727606848952849359738715637
+ 7365178379539482598486067271
step 31: 9092785228492331958224782908
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step 32: 17185659457083664906450655817
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step 33: 89041264918030302981946313988
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step 34: 177972629836950606063892528086
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step 35: 858797928197556665702818807857
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step 36: 1617506746405123321494648605715
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step 37: 6792575211346356536541124662876
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step 38: 13575239422802713072972250415852
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step 39: 39426644650729744793794743673383
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step 40: 77764279400469489586500388335876
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step 41: 145617667701038088082900885582653
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step 42: 501903255710318968913008652299194
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step 43: 993895512510638838726026204608299
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step 44: 1986701915131266677562041420206698
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step 45: 10952722156533924444183356611283589
+ 98538211665338144442933565122725901
step 46: 109490933821872068887116921734009490
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step 47: 204391370951483857747395050073104391
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step 48: 397792741002077605505779209146297793
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step 49: 795585382905055111012549409293595586
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step 50: 1481180775810000321124099918577181183
+ 3811817758199904211230000185770811841
step 51: 5292998534009904532354100104347993024
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step 52: 9496995968019919064708199108706985949
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step 53: 18992892046039837139317398217402982898
+ 89828920471289371393173893064029829981
step 54: 108821812517329208532491291281432812879
+ 978218234182192194235802923715218128801
step 55: 1087040046699521402768294214996650941680
+ 0861490566994124928672041259966400407801
step 56: 1948530613693646331440335474963051349481
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step 57: 3797962117388391661881671938926211707972
+ 2797071126298391761881661938837112697973
step 58: 6595033243686783423763333877763324405945
+ 5495044233677783333673243876863423305956
step 59: 12090077477364566757436577754626747711901
+ 10911774762645777563475766546377477009021
step 60: 23001852240010344320912344301004224720922
+ 22902742240010344321902344301004225810032
step 61: 45904594480020688642814688602008450530954
+ 45903505480020688641824688602008449540954
step 62: 91808099960041377284639377204016900071908
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step 63: 172725100921081654678287654518023899152727
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step 64: 899977099241897111461164110698152900679998
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step 65: 1799953108493793122922328222496295891459996
+ 6999541985926942228232292213973948013599971
step 66: 8799495094420735351154620436470243905059967
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step 67: 16499000187841481691419131971840488811009945
+ 54990011888404817913191419618414878100099461
step 68: 71489012076246299604610551590255366911109406
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step 69: 131979124042601509120112192289519633932207823
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step 70: 460681363379517491411323214194625874354186954
+ 459681453478526491412323114194715973363186064
step 71: 920362816858043982823646328389341847717373018
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step 72: 1730736534606187966647292656678682706335636047
+ 7406365336072868766562927466697816064356370371
step 73: 9137101870679056733210220123376498770692006418
+ 8146002960778946733210220123376509760781017319
step 74: 17283104831458003466420440246753008531473023737
+ 73732037413580035764204402466430085413840138271
step 75: 91015142245038039230624842713183093945313162008
+ 80026131354939038131724842603293083054224151019
step 76: 171041273599977077362349685316476176999537313027
+ 720313735999671674613586943263770779995372140171
step 77: 891355009599648751975936628580246956994909453198
+ 891354909499659642085826639579157846995900553198
step 78: 1782709919099308394061763268159404803990810006396
+ 6936000180993084049518623671604938039909199072871
step 79: 8718710100092392443580386939764342843900009079267
+ 7629709000093482434679396830853442932900010178178
step 80: 16348419100185874878259783770617785776800019257445
+ 54475291000867758771607738795287847858100191484361
step 81: 70823710101053633649867522565905633634900210741806
+ 60814701200943633650956522576894633635010101732807
step 82: 131638411301997267300824045142800267269910312474613
+ 316474213019962762008241540428003762799103114836131
step 83: 448112624321960029309065585570804030069013427310744
+ 447013724310960030408075585560903920069123426211844
step 84: 895126348632920059717141171131707950138136853522588
+ 885225358631831059707131171141717950029236843621598
step 85: 1780351707264751119424272342273425900167373697144186
+ 6814417963737610095243722432724249111574627071530871
step 86: 8594769671002361214667994774997675011742000768675057
+ 7505768670002471105767994774997664121632001769674958
step 87: 16100538341004832320435989549995339133374002538350015
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step 88: 67105921861052165513795984148948741457214016921850176
+ 67105812961041275414784984148959731556125016812950176
step 89: 134211734822093440928580968297908473013339033734800352
+ 253008437330933310374809792869085829044390228437112431
step 90: 387220172153026751303390761166994302057729262171912783
+ 387219171262927750203499661167093303157620351271022783
step 91: 774439343415954501506890422334087605215349613442935566
+ 665539244316943512506780433224098605105459514343934477
step 92: 1439978587732898014013670855558186210320809127786870043
+ 3400786877219080230126818555580763104108982377858799341
step 93: 4840765464951978244140489411138949314429791505645669384
+ 4839665465051979244139498311149840414428791594645670484
step 94: 9680430930003957488279987722288789728858583100291339868
+ 8689331920013858588279878822277899728847593000390340869
step 95: 18369762850017816076559866544566689457706176100681680737
+ 73708618600167160775498666544566895567061871005826796381
step 96: 92078381450184976852058533089133585024768047106508477118
+ 81177480560174086742058533198033585025867948105418387029
step 97: 173255862010359063594117066287167170050635995211926864147
+ 741468629112599536050071761782660711495360953010268552371
step 98: 914724491122958599644188828069827881545996948222195416518
+ 815614591222849699545188728960828881446995859221194427419
step 99: 1730339082345808299189377557030656762992992807443389843937
+ 7393489833447082992992676560307557739819928085432809330371
step 100: 9123828915792891292182054117338214502812920892876199174308
+ 8034719916782980292182054128337114502812921982975198283219
step 101: 17158548832575871584364108245675329005625842875851397457527
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step 102: 89734028148433696437014200603329609151974360733375282042698
+ 89624028257333706347915190692330600241073469633484182043798
step 103: 179358056405767402784929391295660209393047830366859464086496
+ 694680464958663038740393902066592193929487204767504650853971
step 104: 874038521364430441525323293362252403322535035134364114940467
+ 764049411463431530535223304252263392323525144034463125830478
step 105: 1638087932827861972060546597614515795646060179168827240770945
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step 106: 7128858360116481682667012572768683752096662970856109638579306
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step 107: 13168616729133062475333915146637356504204325832702220277167523
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step 108: 45744793931353786327674155712011020656137683258735413038853654
+ 45635883031453785238673165602011021755147672368735313939744754
step 109: 91380676962807571566347321314022042411285355627470726978598408
+ 80489587962707472655358211424022041312374366517570826967608319
step 110: 171870264925515044221705532738044083723659722145041553946206727
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step 111: 899472914280655585449661860118484920959166844585557083408284898
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step 112: 1797955718661411170898323819147969732027333789171113165827559896
+ 6989557285613111719873337202379697419183238980711141668175597971
step 113: 8787513004274522890771661021527667151210572769882254834003157867
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step 114: 16475026008659045780444411143045334402412234540864509558006315745
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step 115: 71226386094249592584987632563488688436523678949618605238068373206
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step 116: 131463772177500274279975265126977376873047357898148199487136735423
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step 117: 456001403962492116178729005505651156494609937870620205258414099554
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step 118: 911991818814994142257468912000302313000110865742231499527718200208
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step 119: 1713994636540988274505036923000615516000330730494472998946536399327
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step 120: 8953930993039981019445407253006770676003627035549201889402901392498
+ 8942931092049881029455307263006760776003527045449101899303990393598
step 121: 17896862085089862048900714516013531452007154080998303788706891786096
+ 69068719860788730389908045170025413531061541700984026898058026869871
step 122: 86965581945878592438808759686038944983068695781982330686764918655967
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step 123: 163921263892647195767727519372077889966137391562865760274619837212935
+ 539212738916472067568265193731669988770273915727767591746298362129361
step 124: 703134002809119263335992713103747878736411307290633352020918199342296
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step 125: 1395377994628139516672085416218385757483712624590166714932826399773603
+ 3063779936282394176610954262173847575838126145802766159318264997735931
step 126: 4459157930910533693283039678392233333321838770392932874251091397509534
+ 4359057931901524782392930778381233333322938769303823963350190397519544
step 127: 8818215862812058475675970456773466666644777539696756837601281795029078
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step 128: 17527421834633125862252939814547933333288554080492522586103464480157266
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step 129: 83802530281063294384782347860136166667263095974417749438237108292629837
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step 130: 157695159561236577879553795819172443333426202848746497787473126496150675
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step 131: 733746854182611365674201644021796776677698121446102476563105292447747426
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step 132: 1358494598475112731348403288143693553355395241892204953126221573906394763
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step 133: 5033430692226338944942426269569629086909358660715253384498337322861343294
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step 134: 9956862374463677889775951440238168183718628320341495878996673545821686599
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step 135: 19913723659917444888561892870476436357537246640783091658884437190554373198
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step 136: 109051069169090893774180931575140709932900714048612908247728909186187105189
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step 137: 1090552850851000721516990148415557719172807755623751989725127000148147256090
+ 0906527418410007215279891573265577082719177555148410996151270001580582550901
step 138: 1997080269261007936796881721681134801891985310772162985876397001728729806991
+ 1996089278271007936785892612770135891981084311861271886976397001629620807991
step 139: 3993169547532015873582774334451270693873069622633434872852794003358350614982
+ 2894160538533004972582784343362269603783960721544334772853785102357459613993
step 140: 6887330086065020846165558677813540297657030344177769645706579105715810228975
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step 141: 12685550271240040602241028355527970605224950797365538201323059311322610566861
+ 16866501622311395032310283556379705942250607972555382014220604004217205558621
step 142: 29552051893551435634551311911907676547475558769920920215543663315539816125482
+ 28452161893551336634551202902996785557474567670911911315543653415539815025592
step 143: 58004213787102772269102514814904462104950126440832831531087316731079631151074
+ 47015113697013761378013513823804462105940126440941841520196227720178731240085
step 144: 105019327484116533647116028638708924210890252881774673051283544451258362391159
+ 951193263852154445382150376477188252098012429807836820611746335611484723910501
step 145: 1056212591336270979029266405115897176308902682689611493663029880062743086301660
+ 0661036803472600889203663941169862862098036717985115046629209790726331952126501
step 146: 1717249394808871868232930346285760038406939400674726540292239670789075038428161
+ 1618248305709870769322920456274760049396048300675826430392328681788084939427171
step 147: 3335497700518742637555850802560520087802987701350552970684568352577159977855332
+ 2335587799517752538654860792550531077892087800250652080585557362478150077945333
step 148: 5671085500036495176210711595111051165695075501601205051270125715055310055800665
+ 5660085500135505175210721505021061055705965611501115951170126715946300055801765
step 149: 11331171000172000351421433100132112221401041113102321002440252431001610111602430
+ 03420611101610013425204420012320131114010412221123100133412415300027100017113311
step 150: 14751782101782013776625853112452243335411453334225421135852667731028710128715741
|
|
100000109584608 takes 150 iterations / steps to resolve into a 80 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.)
Digits | Number | Result |
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 2,531,669 times since Saturday, March 9th, 2002.)
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