REVERSAL-ADDITION
PALINDROME
TEST ON
100017449991820
|
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 100017449991820: |
100017449991820
+ 028199944710001
step 1: 128217394701821
+ 128107493712821
step 2: 256324888414642
+ 246414888423652
step 3: 502739776838294
+ 492838677937205
step 4: 995578454775499
+ 994577454875599
step 5: 1990155909651098
+ 8901569095510991
step 6: 10891725005162089
+ 98026150052719801
step 7: 108917875057881890
+ 098188750578719801
step 8: 207106625636601691
+ 196106636526601702
step 9: 403213262163203393
+ 393302361262312304
step 10: 796515623425515697
+ 796515524326515697
step 11: 1593031147752031394
+ 4931302577411303951
step 12: 6524333725163335345
+ 5435333615273334256
step 13: 11959667340436669601
+ 10696663404376695911
step 14: 22656330744813365512
+ 21556331844703365622
step 15: 44212662589516731134
+ 43113761598526621244
step 16: 87326424188043352378
+ 87325334088142462378
step 17: 174651758276185814756
+ 657418581672857156471
step 18: 832070339949042971227
+ 722179240949933070238
step 19: 1554249580898976041465
+ 5641406798980859424551
step 20: 7195656379879835466016
+ 6106645389789736565917
step 21: 13302301769669572031933
+ 33913027596696710320331
step 22: 47215329366366282352264
+ 46225328266366392351274
step 23: 93440657632732674703538
+ 83530747623723675604439
step 24: 176971405256456350307977
+ 779703053654652504179671
step 25: 956674458911108854487648
+ 846784458801119854476659
step 26: 1803458917712228708964307
+ 7034698078222177198543081
step 27: 8838156995934405907507388
+ 8837057095044395996518388
step 28: 17675214090978801904025776
+ 67752040910887909041257671
step 29: 85427255001866710945283447
+ 74438254901766810055272458
step 30: 159865509903633521000555905
+ 509555000125336309905568951
step 31: 669420510028969830906124856
+ 658421609038969820015024966
step 32: 1327842119067939650921149822
+ 2289411290569397609112487231
step 33: 3617253409637337260033637053
+ 3507363300627337369043527163
step 34: 7124616710264674629077164216
+ 6124617709264764620176164217
step 35: 13249234419529439249253328433
+ 33482335294293492591443294231
step 36: 46731569713822931840696622664
+ 46622669604813922831796513764
step 37: 93354239318636854672493136428
+ 82463139427645863681393245339
step 38: 175817378746282718353886381767
+ 767183688353817282647873718571
step 39: 943001067100100001001760100338
+ 833001067100100001001760100349
step 40: 1776002134200200002003520200687
+ 7860020253002000020024312006771
step 41: 9636022387202200022027832207458
+ 8547022387202200022027832206369
step 42: 18183044774404400044055664413827
+ 72831446655044000440447744038181
step 43: 91014491429448400484503408452008
+ 80025480430548400484492419441019
step 44: 171039971859996800968995827893027
+ 720398728599869008699958179930171
step 45: 891438700459865809668954007823198
+ 891328700459866908568954007834198
step 46: 1782767400919732718237908015657396
+ 6937565108097328172379190047672871
step 47: 8720332509017060890617098063330267
+ 7620333608907160980607109052330278
step 48: 16340666117924221871224207115660545
+ 54506651170242217812242971166604361
step 49: 70847317288166439683467178282264906
+ 60946228287176438693466188271374807
step 50: 131793545575342878376933366553639713
+ 317936355663339673878243575545397131
step 51: 449729901238682552255176942099036844
+ 448630990249671552255286832109927944
step 52: 898360891488354104510463774208964788
+ 887469802477364015401453884198063898
step 53: 1785830693965718119911917658407028686
+ 6868207048567191199118175693960385871
step 54: 8654037742532909319030093352367414557
+ 7554147632533900309139092352477304568
step 55: 16208185375066809628169185704844719125
+ 52191744840758196182690866057358180261
step 56: 68399930215825005810860051762202899386
+ 68399820226715006801850052851203999386
step 57: 136799750442540012612710104613406898772
+ 277898604316401017216210045244057997631
step 58: 414698354758941029828920149857464896403
+ 304698464758941029828920149857453896414
step 59: 719396819517882059657840299714918792817
+ 718297819417992048756950288715918693917
step 60: 1437694638935874108414790588430837486734
+ 4376847380348850974148014785398364967341
step 61: 5814542019284725082562805373829202454075
+ 5704542029283735082652805274829102454185
step 62: 11519084048568460165215610648658304908260
+ 06280940385684601651256106486584048091511
step 63: 17800024434253061816471717135242352999771
+ 17799925324253171717461816035243442000871
step 64: 35599949758506233533933533170485795000642
+ 24600059758407133533933533260585794999553
step 65: 60200009516913367067867066431071590000195
+ 59100009517013466076876076331961590000206
step 66: 119300019033926833144743142763033180000401
+ 104000081330367241347441338629330910003911
step 67: 223300100364294074492184481392364090004312
+ 213400090463293184481294470492463001003322
step 68: 436700190827587258973478951884827091007634
+ 436700190728488159874379852785728091007634
step 69: 873400381556075418847858804670555182015268
+ 862510281555076408858748814570655183004378
step 70: 1735910663111151827706607619241210365019646
+ 6469105630121429167066077281511113660195371
step 71: 8205016293232580994772684900752324025215017
+ 7105125204232570094862774990852323926105028
step 72: 15310141497465151089635459891604647951320045
+ 54002315974640619895453698015156479414101351
step 73: 69312457472105770985089157906761127365421396
+ 69312456372116760975198058907750127475421396
step 74: 138624913844222531960287216814511254840842792
+ 297248048452115418612782069135222448319426831
step 75: 435872962296337950573069285949733703160269623
+ 326962061307337949582960375059733692269278534
step 76: 762835023603675900156029661009467395429548157
+ 751845924593764900166920651009576306320538267
step 77: 1514680948197440800322950312019043701750086424
+ 4246800571073409102130592230080447918490864151
step 78: 5761481519270849902453542542099491620240950575
+ 5750590420261949902452453542099480729151841675
step 79: 11512071939532799804905996084198972349392792250
+ 05229729394327989148069950940899723593917021511
step 80: 16741801333860788952975947025098695943309813761
+ 16731890334959689052074957925988706833310814761
step 81: 33473691668820478005050904951087402776620628522
+ 22582602667720478015940905050087402886619637433
step 82: 56056294336540956020991810001174805663240265955
+ 55956204236650847110001819902065904563349265065
step 83: 112012498573191803130993629903240710226589531020
+ 020135985622017042309926399031308191375894210211
step 84: 132148484195208845440920028934548901602483741231
+ 132147384206109845439820029044548802591484841231
step 85: 264295868401318690880740057979097704193968582462
+ 264285869391407790979750047088096813104868592462
step 86: 528581737792726481860490105067194517298837174924
+ 429471738892715491760501094068184627297737185825
step 87: 958053476685441973620991199135379144596574360749
+ 947063475695441973531991199026379144586674350859
step 88: 1905116952380883947152982398161758289183248711608
+ 8061178423819828571618932892517493880832596115091
step 89: 9966295376200712518771915290679252170015844826699
+ 9966284485100712529760925191778152170026735926699
step 90: 19932579861301425048532840482457404340042580753398
+ 89335708524004340475428404823584052410316897523991
step 91: 109268288385305765523961245306041456750359478277389
+ 983772874953057654140603542169325567503583882862901
step 92: 1093041163338363419664564787475367024253943361140290
+ 0920411633493524207635747874654669143638333611403901
step 93: 2013452796831887627300312662130036167892276972544191
+ 1914452796722987616300312662130037267881386972543102
step 94: 3927905593554875243600625324260073435773663945087293
+ 3927805493663775343700624235260063425784553955097293
step 95: 7855711087218650587301249559520136861558217900184586
+ 6854810097128551686310259559421037850568127801175587
step 96: 14710521184347202273611509118941174712126345701360173
+ 37106310754362121747114981190511637220274348112501741
step 97: 51816831938709324020726490309452811932400693813861914
+ 41916831839600423911825490309462702042390783913861815
step 98: 93733663778309747932551980618915513974791477727723729
+ 92732772777419747931551981608915523974790387736633739
step 99: 186466436555729495864103962227831037949581865464357468
+ 864753464568185949730138722269301468594927555634664681
step 100: 1051219901123915445594242684497132506544509421099022149
+ 9412209901249054456052317944862424955445193211099121501
step 101: 10463429802372969901646560629359557461989702632198143650
+ 05634189123620798916475595392606564610996927320892436401
step 102: 16097618925993768818122156021966122072986629953090580051
+ 15008509035992668927022166912065122181886739952981679061
step 103: 31106127961986437745144322934031244254873369906072259112
+ 21195227060996337845244213043922344154773468916972160113
step 104: 52301355022982775590388535977953588409646838823044419225
+ 52291444032883864690488535977953588309557728922055310325
step 105: 104592799055866640280877071955907176719204567745099729550
+ 055927990547765402917671709559170778082046668550997295401
step 106: 160520789603632043198548781515077954801251236296097024951
+ 159420790692632152108459770515187845891340236306987025061
step 107: 319941580296264195307008552030265800692591472603084050012
+ 210050480306274195296008562030255800703591462692085149913
step 108: 529992060602538390603017114060521601396182935295169199925
+ 529991961592539281693106125060411710306093835206060299925
step 109: 1059984022195077672296123239120933311702276770501229499850
+ 0589949221050776722071133390219323216922767705912204899501
step 110: 1649933243245854394367256629340256528625044476413434399351
+ 1539934343146744405268256520439266527634934585423423399461
step 111: 3189867586392598799635513149779523056259979061836857798812
+ 2188977586381609799526503259779413155369978952936857689813
step 112: 5378845172774208599162016409558936211629958014773715488625
+ 5268845173774108599261126398559046102619958024772715488735
step 113: 10647690346548317198423142808117982314249916039546430977360
+ 06377903464593061994241328971180824132489171384564309674601
step 114: 17025593811141379192664471779298806446739087424110740651961
+ 16915604701142478093764460889297717446629197314111839552071
step 115: 33941198512283857286428932668596523893368284738222580204032
+ 23040208522283748286339832569586623982468275838221589114933
step 116: 56981407034567605572768765238183147875836560576444169318965
+ 56981396144467506563857874138183256786727550676543070418965
step 117: 113962803179035112136626639376366404662564111252987239737930
+ 039737932789252111465266404663673936626631211530971308269311
step 118: 153700735968287223601893044040040341289195322783958548007241
+ 142700845859387223591982143040040440398106322782869537007351
step 119: 296401581827674447193875187080080781687301645566828085014592
+ 295410580828665546103786187080080781578391744476728185104692
step 120: 591812162656339993297661374160161563265693390043556270119284
+ 482911072655340093396562365161061473166792399933656261218195
step 121: 1074723235311680086694223739321223036432485789977212531337479
+ 9747331352127799875842346303221239373224966800861135323274701
step 122: 10822054587439479962536570042542462409657452590838347854612180
+ 08121645874383809525475690426424524007563526997493478545022801
step 123: 18943700461823289488012260468966986417220979588331826399634981
+ 18943699362813388597902271468966986406221088498232816400734981
step 124: 37887399824636678085914531937933972823442068086564642800369962
+ 26996300824646568086024432827933973913541958087663642899378873
step 125: 64883700649283246171938964765867946736984026174228285699748835
+ 53884799658282247162048963764976856746983917164238294600738846
step 126: 118768500307565493333987928530844803483967943338466580300487681
+ 186784003085664833349769384308448035829789333394565703005867811
step 127: 305552503393230326683757312839292839313757276733032283306355492
+ 294553603382230337672757313938292938213757386623032393305255503
step 128: 600106106775460664356514626777585777527514663356064676611610995
+ 599016116676460653366415725777585777626415653466064577601601006
step 129: 1199122223451921317722930352555171555153930316822129254213212001
+ 1002123124529212286130393515551715552530392277131291543222219911
step 130: 2201245347981133603853323868106887107684322593953420797435431912
+ 2191345347970243593952234867017886018683233583063311897435421022
step 131: 4392590695951377197805558735124773126367556177016732694870852934
+ 4392580784962376107716557636213774215378555087917731595960952934
step 132: 8785171480913753305522116371338547341746111264934464290831805868
+ 8685081380924644394621116471437458331736112255033573190841715878
step 133: 17470252861838397700143232842776005673482223519968037481673521746
+ 64712537618473086991532228437650067724823234100779383816825207471
step 134: 82182790480311484691675461280426073398305457620747421298498729217
+ 71292789489212474702675450389337062408216457619648411308409728128
step 135: 153475579969523959394350911669763135806521915240395832606908457345
+ 543754809606238593042519125608531367966119053493959325969975574351
step 136: 697230389575762552436870037278294503772640968734355158576884031696
+ 696130488675851553437869046277305492872730078634255267575983032796
step 137: 1393360878251614105874739083555599996645371047368610426152867064492
+ 2944607682516240168637401735466999955553809374785014161528780633931
step 138: 4337968560767854274512140819022599952199180422153624587681647698423
+ 3248967461867854263512240819912599952209180412154724587670658697334
step 139: 7586936022635708538024381638935199904408360834308349175352306395757
+ 7575936032535719438034380638044099915398361834208358075362206396857
step 140: 15162872055171427976058762276979299819806722668516707250714512792614
+ 41629721541705270761586622760891899297967226785067972417155027826151
step 141: 56792593596876698737645385037871199117773949453584679667869540618765
+ 56781604596876697648535494937771199117873058354673789667869539529765
step 142: 113574198193753396386180879975642398235647007808258469335739080148530
+ 035841080937533964852808700746532893246579978081683693357391891475311
step 143: 149415279131287361238989580722175291482226985889942162693130971623841
+ 148326179031396261249988589622284192571227085989832163782131972514941
step 144: 297741458162683622488978170344459484053454071879774326475262944138782
+ 287831449262574623477978170454350484954443071879884226386261854147792
step 145: 585572907425258245966956340798809969007897143759658552861524798286574
+ 475682897425168255856957341798700969908897043659669542852524709275585
step 146: 1061255804850426501823913682597510938916794187419328095714049507562159
+ 9512657059404175908239147814976198390157952863193281056240584085521601
step 147: 10573912864254602410063061497573709329074747050612609151954633593083760
+ 06738039533645915190621605074747092390737579416036001420645246821937501
step 148: 17311952397900517600684666572320801719812326466648610572599880415021261
+ 16212051408899527501684666462321891710802327566648600671500979325911371
step 149: 33524003806800045102369333034642693430614654033297211244100859740932632
+ 23623904795800144211279233045641603439624643033396320154000860830042533
step 150: 57147908602600189313648566080284296870239297066693531398101720570975165
+ 56157907502710189313539666079293207869248208066584631398100620680974175
step 151: 113305816105310378627188232159577504739487505133278162796202341251949340
+ 043949152143202697261872331505784937405775951232881726873013501618503311
step 152: 157254968248513075889060563665362442145263456366159889669215842870452651
+ 156254078248512966988951663654362541244263566365060988570315842869452751
step 153: 313509046497026042878012227319724983389527022731220878239531685739905402
+ 204509937586135932878022137220725983389427913722210878240620794640905313
step 154: 518018984083161975756034364540450966778954936453431756480152480380810715
+ 517018083084251084657134354639459877669054045463430657579161380489810815
step 155: 1035037067167413060413168719179910844448008981916862414059313860870621530
+ 0351260780683139504142686191898008444480199719178613140603147617607305301
step 156: 1386297847850552564555854911077919288928208701095475554662461478477926831
+ 1386297748741642664555745901078028298829197701194585554652550587487926831
step 157: 2772595596592195229111600812155947587757406402290061109315012065965853662
+ 2663585695602105139011600922046047577857495512180061119225912956955952772
step 158: 5436181292194300368123201734201995165614901914470122228540925022921806434
+ 4346081292205290458222210744191094165615991024371023218630034912921816345
step 159: 9782262584399590826345412478393089331230892938841145447170959935843622779
+ 9772263485399590717445411488392980321339803938742145436280959934852622879
step 160: 19554526069799181543790823966786069652570696877583290883451919870696245658
+ 85654269607891915438809238577869607525696068766932809734518199796062545591
step 161: 105208795677691096982600062544655677178266765644516100617970119666758791249
+ 942197857666911079716001615446567662871776556445260006289690196776597802501
step 162: 1047406653344602176698601677991223340050043322089776106907660316443356593750
+ 0573956533446130667096016779802233400500433221997761068966712064433566047401
step 163: 1621363186790732843794618457793456740550476544087537175874372380876922641151
+ 1511462296780832734785717357804456740550476543977548164973482370976813631261
step 164: 3132825483571565578580335815597913481100953088065085340847854751853736272412
+ 2142726373581574587480435805608803590011843197955185330858755651753845282313
step 165: 5275551857153140166060771621206717071112796286020270671706610403607581554725
+ 5274551857063040166071760720206826972111707176021261770606610413517581555725
step 166: 10550103714216180332132532341413544043224503462041532442313220817125163110450
+ 05401136152171802231324423514026430542234044531414323523123308161241730105501
step 167: 15951239866387982563456955855439974585458547993455855965436528978366893215951
|
|
100017449991820 takes 167 iterations / steps to resolve into a 77 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 2,547,022 times since Saturday, March 9th, 2002.)
|