|
REVERSAL-ADDITION
PALINDROME
TEST ON
14104229999995
|
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 14104229999995: |
14104229999995
+ 59999992240141
step 1: 74104222240136
+ 63104222240147
step 2: 137208444480283
+ 382084444802731
step 3: 519292889283014
+ 410382988292915
step 4: 929675877575929
+ 929575778576929
step 5: 1859251656152858
+ 8582516561529581
step 6: 10441768217682439
+ 93428671286714401
step 7: 103870439504396840
+ 048693405934078301
step 8: 152563845438475141
+ 141574834548365251
step 9: 294138679986840392
+ 293048689976831492
step 10: 587187369963671884
+ 488176369963781785
step 11: 1075363739927453669
+ 9663547299373635701
step 12: 10738911039301089370
+ 07398010393011983701
step 13: 18136921432313073071
+ 17037031323412963181
step 14: 35173952755726036252
+ 25263062755725937153
step 15: 60437015511451973405
+ 50437915411551073406
step 16: 110874930923003046811
+ 118640300329039478011
step 17: 229515231252042524822
+ 228425240252132515922
step 18: 457940471504175040744
+ 447040571405174049754
step 19: 904981042909349090498
+ 894090943909240189409
step 20: 1799071986818589279907
+ 7099729858186891709971
step 21: 8898801845005480989878
+ 8789890845005481088988
step 22: 17688692690010962078866
+ 66887026901009629688671
step 23: 84575719591020591767537
+ 73576719502019591757548
step 24: 158152439093040183525085
+ 580525381040390934251851
step 25: 738677820133431117776936
+ 639677711134331028776837
step 26: 1378355531267762146553773
+ 3773556412677621355538731
step 27: 5151911943945383502092504
+ 4052902053835493491191515
step 28: 9204813997780876993284019
+ 9104823996780877993184029
step 29: 18309637994561754986468048
+ 84086468945716549973690381
step 30: 102396106940278304960158429
+ 924851069403872049601693201
step 31: 1027247176344150354561851630
+ 0361581654530514436717427201
step 32: 1388828830874664791279278831
+ 1388729721974664780388288831
step 33: 2777558552849329571667567662
+ 2667657661759239482558557772
step 34: 5445216214608569054226125434
+ 4345216224509658064126125445
step 35: 9790432439118227118352250879
+ 9780522538117228119342340979
step 36: 19570954977235455237694591858
+ 85819549673255453277945907591
step 37: 105390504650490908515640499449
+ 944994046515809094056405093501
step 38: 1050384551166300002572045592950
+ 0592955402752000036611554830501
step 39: 1643339953918300039183600423451
+ 1543240063819300038193599333461
step 40: 3186580017737600077377199756912
+ 2196579917737700067377100856813
step 41: 5383159935475300144754300613725
+ 5273160034574410035745399513835
step 42: 10656319970049710180499700127560
+ 06572100799408101794007991365601
step 43: 17228420769457811974507691493161
+ 16139419670547911875496702482271
step 44: 33367840440005723850004393975432
+ 23457939340005832750004404876333
step 45: 56825779780011556600008798851765
+ 56715889780000665511008797752865
step 46: 113541669560012222111017596604630
+ 036406695710111222210065966145311
step 47: 149948365270123444321083562749941
+ 149947265380123444321072563849941
step 48: 299895630650246888642156126599882
+ 288995621651246888642056036598992
step 49: 588891252301493777284212163198874
+ 478891361212482777394103252198885
step 50: 1067782613513976554678315415397759
+ 9577935145138764556793153162877601
step 51: 10645717758652741111471468578275360
+ 06357287586417411114725685771754601
step 52: 17003005345070152226197154350029961
+ 16992005345179162225107054350030071
step 53: 33995010690249314451304208700060032
+ 23006000780240315441394209601059933
step 54: 57001011470489629892698418301119965
+ 56991110381489629892698407411010075
step 55: 113992121851979259785396825712130040
+ 040031217528693587952979158121299311
step 56: 154023339380672847738375983833429351
+ 153924338389573837748276083933320451
step 57: 307947677770246685486652067766749802
+ 208947667760256684586642077776749703
step 58: 516895345530503370073294145543499505
+ 505994345541492370073305035543598615
step 59: 1022889691071995740146599181087098120
+ 0218907801819956410475991701969882201
step 60: 1241797492891952150622590883056980321
+ 1230896503880952260512591982947971421
step 61: 2472693996772904411135182866004951742
+ 2471594006682815311144092776993962742
step 62: 4944288003455719722279275642998914484
+ 4844198992465729722279175543008824494
step 63: 9788486995921449444558451186007738978
+ 8798377006811548554449441295996848879
step 64: 18586864002732997999007892482004587857
+ 75878540028429870099979923720046868581
step 65: 94465404031162868098987816202051456438
+ 83465415020261878989086826113040456449
step 66: 177930819051424747088074642315091912887
+ 788219190513246470880747424150918039771
step 67: 966150009564671217968822066466009952658
+ 856259900664660228869712176465900051669
step 68: 1822409910229331446838534242931910004327
+ 7234000191392424358386441339220199042281
step 69: 9056410101621755805224975582152109046608
+ 8066409012512855794225085571261010146509
step 70: 17122819114134611599450061153413119193117
+ 71139191131435116005499511643141191822171
step 71: 88262010245569727604949572796554311015288
+ 88251011345569727594940672796554201026288
step 72: 176513021591139455199890245593108512041576
+ 675140215801395542098991554931195120315671
step 73: 851653237392534997298881800524303632357247
+ 742753236303425008188892799435293732356158
step 74: 1594406473695960005487774599959597364713405
+ 5043174637959599954777845000695963746044951
step 75: 6637581111655559960265619600655561110758356
+ 6538570111655560069165620699555561111857366
step 76: 13176151223311120029431240300211122222615722
+ 22751622222111200304213492002111332215167131
step 77: 35927773445422320333644732302322454437782853
+ 35828773445422320323744633302322454437772953
step 78: 71756546890844640657389365604644908875555806
+ 60855557880944640656398375604644809864565717
step 79: 132612104771789281313787741209289718740121523
+ 325121047817982902147787313182987177401216231
step 80: 457733152589772183461575054392276896141337754
+ 457733141698672293450575164381277985251337754
step 81: 915466294288444476912150218773554881392675508
+ 805576293188455377812051219674444882492664519
step 82: 1721042587476899854724201438447999763885340027
+ 7200435883679997448341024274589986747852401271
step 83: 8921478471156897303065225713037986511737741298
+ 8921477371156897303175225603037986511748741298
step 84: 17842955842313794606240451316075973023486482596
+ 69528468432037957061315404260649731324855924871
step 85: 87371424274351751667555855576725704348342407467
+ 76470424384340752767555855576615715347242417378
step 86: 163841848658692504435111711153341419695584824845
+ 548428485596914143351117111534405296856848148361
step 87: 712270334255606647786228822687746716552432973206
+ 602379234255617647786228822687746606552433072217
step 88: 1314649568511224295572457645375493323104866045423
+ 3245406684013233945735467542755924221158659464131
step 89: 4560056252524458241307925188131417544263525509554
+ 4559055253624457141318815297031428544252526500654
step 90: 9119111506148915382626740485162846088516052010208
+ 8020102506158806482615840476262835198416051119119
step 91: 17139214012307721865242580961425681286932103129327
+ 72392130123968218652416908524256812770321041293171
step 92: 89531344136275940517659489485682494057253144422498
+ 89422444135275049428658498495671504957263144313598
step 93: 178953788271550989946317987981353999014516288736096
+ 690637882615410999353189789713649989055172887359871
step 94: 869591670886961989299507777695003988069689176095967
+ 769590671986960889300596777705992989169688076195968
step 95: 1639182342873922878600104555400996977239377252291935
+ 5391922527739327796990045554010068782293782432819361
step 96: 7031104870613250675590150109411065759533159685111296
+ 6921115869513359575601149010510955760523160784011307
step 97: 13952220740126610251191299119922021520056320469122603
+ 30622196402365002512022991199219115201662104702225931
step 98: 44574417142491612763214290319141136721718425171348534
+ 43584317152481712763114191309241236721619424171447544
step 99: 88158734294973325526328481628382373443337849342796078
+ 87069724394873334437328382618482362552337949243785188
step 100: 175228458689846659963656864246864735995675798586581266
+ 662185685897576599537468642468656369956648986854822571
step 101: 837414144587423259501125506715521105952324785441403837
+ 738304144587423259501125517605521105952324785441414738
step 102: 1575718289174846519002251024321042211904649570882818575
+ 5758182880759464091122401234201522009156484719828175751
step 103: 7333901169934310610124652258522564221061134290710994326
+ 6234990170924311601224652258522564210160134399611093337
step 104: 13568891340858622211349304517045128431221268690322087663
+ 36678022309686212213482154071540394311222685804319886531
step 105: 50246913650544834424831458588585522742443954494641974194
+ 49147914649445934424722558588585413842443844505631964205
step 106: 99394828299990768849554017177170936584887799000273938399
+ 99383937200099778848563907177171045594886709999282849399
step 107: 198778765500090547698117924354341982179774508999556787798
+ 897787655999805477971289143453429711896745090005567877891
step 108: 1096566421499896025669407067807771694076519599005124665689
+ 9865664215009959156704961777087607049665206989941246656901
step 109: 10962230636509855182374368844895378743741726588946371322590
+ 09522317364988562714734787359844886347328155890563603226901
step 110: 20484548001498417897109156204740265091069882479509974549491
+ 19494547990597428896019056204740265190179871489410084548402
step 111: 39979095992095846793128212409480530281249753968920059097893
+ 39879095002986935794218203508490421282139764859029959097993
step 112: 79858190995082782587346415917970951563389518827950018195886
+ 68859181005972881598336515907971951464378528728059909185897
step 113: 148717372001055664185682931825942903027768047556009927381783
+ 387183729900655740867720309249528139286581466550100273717841
step 114: 535901101901711405053403241075471042314349514106110201099624
+ 426990102011601415943413240174570142304350504117109101109535
step 115: 962891203913312820996816481250041184618700018223219302209159
+ 951902203912322810007816481140052184618699028213319302198269
step 116: 1914793407825635631004632962390093369237399046436538604407428
+ 8247044068356346409937329633900932692364001365365287043974191
step 117: 10161837476181982040941962596291026061601400411801825648381619
+ 91618384652810811400410616062019269526914904028918167473816101
step 118: 101780222128992793441352578658310295588516304440719993122197720
+ 027791221399917044403615885592013856875253144397299821222087101
step 119: 129571443528909837844968464250324152463769448838019814344284821
+ 128482443418910838844967364251423052464869448738909825344175921
step 120: 258053886947820676689935828501747204928638897576929639688460742
+ 247064886936929675798836829402747105828539986676028749688350852
step 121: 505118773884750352488772657904494310757178884252958389376811594
+ 495118673983859252488871757013494409756277884253057488377811505
step 122: 1000237447868609604977644414917988720513456768506015877754623099
+ 9903264577785106058676543150278897194144467794069068687447320001
step 123: 10903502025653715663654187565196885914657924562575084565201943100
+ 00134910256548057526542975641958869156578145636651735652020530901
step 124: 11038412282201773190197163207155755071236070199226820217222474001
+ 10047422271202862299107063217055755170236179109137710228221483011
step 125: 21085834553404635489304226424211510241472249308364530445443957012
+ 21075934454403546380394227414201511242462240398453640435543858012
step 126: 42161769007808181869698453838413021483934489706818170880987815024
+ 42051878908807181860798443938412031483835489696818180870096716124
step 127: 84213647916615363730496897776825052967769979403636351751084531148
+ 84113548015715363630497996776925052867779869403736351661974631248
step 128: 168327195932330727360994894553750105835549848807372703413059162396
+ 693261950314307273708848945538501057355498499063727033239591723861
step 129: 861589146246638001069843840092251163191048347871099736652650886257
+ 752688056256637990178743840191361152290048348960100836642641985168
step 130: 1614277202503275991248587680283612315481096696831200573295292871425
+ 5241782925923750021386966901845132163820867858421995723052027724161
step 131: 6856060128427026012635554582128744479301964555253196296347320595586
+ 6855950237436926913525554691039744478212854555362106207248210606586
step 132: 13712010365863952926161109273168488957514819110615302503595531202172
+ 27120213559530520351601191841575988486137290116162925936856301021731
step 133: 40832223925394473277762301114744477443652109226778228440451832223903
+ 30932223815404482287762290125634477444741110326777237449352932223804
step 134: 71764447740798955565524591240378954888393219553555465889804764447707
+ 70774446740898856455535591239388845987304219542556555989704774446717
step 135: 142538894481697812021060182479767800875697439096112021879509538894424
+ 424498835905978120211690934796578008767974281060120218796184498835241
step 136: 567037730387675932232751117276345809643671720156232240675694037729665
+ 566927730496576042232651027176346908543672711157232239576783037730765
step 137: 1133965460884251974465402144452692718187344431313464480252477075460430
+ 0340645707742520844643131344437818172962544412045644791524880645693311
step 138: 1474611168626772819108533488890510891149888843359109271777357721153741
+ 1473511277537771729019533488889411980150988843358019182776268611164741
step 139: 2948122446164544548128066977779922871300877686717128454553626332318482
+ 2848132336263554548217176867780031782299777796608218454454616442218492
step 140: 5796254782428099096345243845559954653600655483325346909008242774536974
+ 4796354772428009096435233845560063564599555483425436909908242874526975
step 141: 10592609554856108192780477691120018218200210966750783818916485649063949
+ 94936094658461981838705766901200281281002119677408729180165845590629501
step 142: 105528704213318090031486244592320299499202330644159512999082331239693450
+ 054396932133280999215951446033202994992023295442684130090813312407825501
step 143: 159925636346599089247437690625523294491225626086843643089895643647518951
+ 159815746346598980346348680626522194492325526096734742980995643636529951
step 144: 319741382693198069593786371252045488983551152183578386070891287284048902
+ 209840482782198070683875381251155389884540252173687395960891396283147913
step 145: 529581865475396140277661752503200878868091404357265782031782683567196815
+ 518691765386287130287562753404190868878002305257166772041693574568185925
step 146: 1048273630861683270565224505907391747746093709614432554073476258135382740
+ 0472835318526743704552344169073906477471937095054225650723861680363728401
step 147: 1521108949388426975117568674981298225218030804668658204797337938499111141
+ 1411119948397337974028568664080308125228921894768657115796248839498011251
step 148: 2932228897785764949146137339061606350446952699437315320593586777997122392
+ 2932217997776853950235137349962596440536061609337316419494675877988222392
step 149: 5864446895562618899381274689024202790983014308774631740088262655985344784
+ 4874435895562628800471364778034103890972024209864721839988162655986444685
step 150: 10738882791125247699852639467058306681955038518639353580076425311971789469
+ 96498717911352467008535393681583055918660385076493625899674252119728883701
step 151: 107237600702477714708388033148641362600615423595132979479750677431700673170
+ 071376007134776057974979231595324516006263146841330883807417774207006732701
step 152: 178613607837253772683367264743965878606878570436463863287168451638707405871
+ 178504707836154861782368364634075878606878569347462763386277352738706316871
step 153: 357118315673408634465735629378041757213757139783926626673445804377413722742
+ 247227314773408544376626629387931757312757140873926537564436804376513811753
step 154: 604345630446817178842362258765973514526514280657853164237882608753927534495
+ 594435729357806288732461358756082415625415379567852263248871718644036543406
step 155: 1198781359804623467574823617522055930151929660225705427486754327397964077901
+ 1097704697937234576847245075220669291510395502257163284757643264089531878911
step 156: 2296486057741858044422068692742725221662325162482868712244397591487495956812
+ 2186595947841957934422178682842615232661225272472968602244408581477506846922
step 157: 4483082005583815978844247375585340454323550434955837314488806172965002803734
+ 4373082005692716088844137385594340553234540435855737424488795183855002803844
step 158: 8856164011276532067688384761179681007558090870811574738977601356820005607578
+ 8757065000286531067798374751180780908557001869711674838867602356721104616588
step 159: 17613229011563063135486759512360461916115092740523249577845203713541110224166
+ 66142201114531730254877594232504729051161916406321595768453136036511092231671
step 160: 83755430126094793390364353744865190967277009146844845346298339750052202455837
+ 73855420225005793389264354844864190077276909156844735346309339749062103455738
step 161: 157610850351100586779628708589729381044553918303689580692607679499114305911575
+ 575119503411994976706296085986303819355440183927985807826977685001153058016751
step 162: 732730353763095563485924794576033200399994102231675388519585364500267363928326
+ 623829363762005463585915883576132201499993002330675497429584365590367353037237
step 163: 1356559717525101027071840678152165401899987104562350885949169730090634716965563
+ 3655696174360900379619495880532654017899981045612518760481707201015257179556531
step 164: 5012255891886001406691336558684819419799968150174869646430876931105891896522094
+ 4902256981985011396780346469684710518699979149184868556331966041006881985522105
step 165: 9914512873871012803471683028369529938499947299359738202762842972112773882044199
+ 9914402883772112792482672028379539927499948399259638203861743082101783782154199
step 166: 19828915757643125595954355056749069865999895698619376406624586054214557664198398
+ 89389146675541245068542660467391689659899956896094765055345959552134675751982891
step 167: 109218062433184370664497015524140759525899852594714141461970545606349233416181289
+ 982181614332943606545079164141417495258998525957041425510794466073481334260812901
step 168: 1091399676766127977209576179665558254784898378551755566972765011679830567676994190
+ 0914996767650389761105672796655571558738984874528555669716759027797216676769931901
step 169: 2006396444416517738315248976321129813523883253080311236689524039477047244446926091
+ 1906296444427407749304259866321130803523883253189211236798425138377156144446936002
step 170: 3912692888843925487619508842642260617047766506269522473487949177854203388893862093
+ 3902683988833024587719497843742259626056677407160622462488059167845293488882962193
step 171: 7815376877676950075339006686384520243104443913430144935976008345699496877776824286
+ 6824286777786949965438006795394410343193444013420254836866009335700596767786735187
step 172: 14639663655463900040777013481778930586297887926850399772842017681400093645563559473
+ 37495536554639000418671024827799305862978879268503987718431077704000936455636693641
step 173: 52135200210102900459448038309578236449276767195354387491273095385401030101200253114
+ 41135200210103010458359037219478345359176767294463287590383084495400920101200253125
step 174: 93270400420205910917807075529056581808453534489817675081656179880801950202400506239
+ 93260500420205910808897165618057671898443535480818565092557070871901950202400407239
step 175: 186530900840411821726704241147114253706897069970636240174213250752703900404800913478
+ 874319008404009307257052312471042636079960798607352411741142407627128114048009035681
step 176: 1060849909244421128983756553618156889786857868577988651915355658379832014452809949159
+ 9519499082544102389738565535191568897758687586879886518163556573898211244429099480601
step 177: 10580348991788523518722322088809725787545545455457875170078912232278043258881909429760
+ 06792490918885234087223221987007157875455454554578752790888022322781532588719984308501
step 178: 17372839910673757605945544075816883663001000010036627960966934555059575847601893738261
+ 16283739810674857595055543966906972663001000010036638861857044554950675737601993827371
step 179: 33656579721348615201001088042723856326002000020073266822823979110010251585203887565632
+ 23656578830258515201001197932822866237002000020062365832724088010010251684312797565633
step 180: 57313158551607130402002285975546722563004000040135632655548067120020503269516685131265
+ 56213158661596230502002176084555623653104000040036522764557958220020403170615585131375
step 181: 113526317213203360904004462060102346216108000080172155420106025340040906440132270262640
+ 046262072231044609040043520601024551271080000801612643201060264400409063302312713625311
step 182: 159788389444247969944047982661126897487188000881784798621166289740449969742444983887951
|
|
|
14104229999995 takes 182 iterations / steps to resolve into a 87 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 2,542,033 times since Saturday, March 9th, 2002.)
|