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                    REVERSAL-ADDITION PALINDROME TEST ON 16002897892

                    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 16002897892:
                    16002897892
                    + 29879820061
                    step 1: 45882717953
                    + 35971728854
                    step 2: 81854446807
                    + 70864445818
                    step 3: 152718892625
                    + 526298817251
                    step 4: 679017709876
                    + 678907710976
                    step 5: 1357925420852
                    + 2580245297531
                    step 6: 3938170718383
                    + 3838170718393
                    step 7: 7776341436776
                    + 6776341436777
                    step 8: 14552682873553
                    + 35537828625541
                    step 9: 50090511499094
                    + 49099411509005
                    step 10: 99189923008099
                    + 99080032998199
                    step 11: 198269956006298
                    + 892600659962891
                    step 12: 1090870615969189
                    + 9819695160780901
                    step 13: 10910565776750090
                    + 09005767756501901
                    step 14: 19916333533251991
                    + 19915233533361991
                    step 15: 39831567066613982
                    + 28931666076513893
                    step 16: 68763233143127875
                    + 57872134133236786
                    step 17: 126635367276364661
                    + 166463672763536621
                    step 18: 293099040039901282
                    + 282109930040990392
                    step 19: 575208970080891674
                    + 476198080079802575
                    step 20: 1051407050160694249
                    + 9424960610507041501
                    step 21: 10476367660667735750
                    + 05753776606676367401
                    step 22: 16230144267344103151
                    + 15130144376244103261
                    step 23: 31360288643588206412
                    + 21460288534688206313
                    step 24: 52820577178276412725
                    + 52721467287177502825
                    step 25: 105542044465453915550
                    + 055519354564440245501
                    step 26: 161061399029894161051
                    + 150161498920993160161
                    step 27: 311222897950887321212
                    + 212123788059798222113
                    step 28: 523346686010685543325
                    + 523345586010686643325
                    step 29: 1046692272021372186650
                    + 0566812731202722966401
                    step 30: 1613505003224095153051
                    + 1503515904223005053161
                    step 31: 3117020907447100206212
                    + 2126020017447090207113
                    step 32: 5243040924894190413325
                    + 5233140914984290403425
                    step 33: 10476181839878480816750
                    + 05761808487893818167401
                    step 34: 16237990327772298984151
                    + 15148989227772309973261
                    step 35: 31386979555544608957412
                    + 21475980644555597968313
                    step 36: 52862960200100206925725
                    + 52752960200100206926825
                    step 37: 105615920400200413852550
                    + 055258314002004029516501
                    step 38: 160874234402204443369051
                    + 150963344402204432478061
                    step 39: 311837578804408875847112
                    + 211748578804408875738113
                    step 40: 523586157608817751585225
                    + 522585157718806751685325
                    step 41: 1046171315327624503270550
                    + 0550723054267235131716401
                    step 42: 1596894369594859634986951
                    + 1596894369584959634986951
                    step 43: 3193788739179819269973902
                    + 2093799629189719378873913
                    step 44: 5287588368369538648847815
                    + 5187488468359638638857825
                    step 45: 10475076836729177287705640
                    + 04650778277192763867057401
                    step 46: 15125855113921941154763041
                    + 14036745114912931155852151
                    step 47: 29162600228834872310615192
                    + 29151601327843882200626192
                    step 48: 58314201556678754511241384
                    + 48314211545787665510241385
                    step 49: 106628413102466420021482769
                    + 967284120024664201314826601
                    step 50: 1073912533127130621336309370
                    + 0739036331260317213352193701
                    step 51: 1812948864387447834688503071
                    + 1703058864387447834688492181
                    step 52: 3516007728774895669376995252
                    + 2525996739665984778277006153
                    step 53: 6042004468440880447654001405
                    + 5041004567440880448644002406
                    step 54: 11083009035881760896298003811
                    + 11830089269806718853090038011
                    step 55: 22913098305688479749388041822
                    + 22814088394797488650389031922
                    step 56: 45727186700485968399777073744
                    + 44737077799386958400768172754
                    step 57: 90464264499872926800545246498
                    + 89464254500862927899446246409
                    step 58: 179928519000735854699991492907
                    + 709294199996458537000915829971
                    step 59: 889222718997194391700907322878
                    + 878223709007193491799817222988
                    step 60: 1767446428004387883500724545866
                    + 6685454270053887834008246447671
                    step 61: 8452900698058275717508970993537
                    + 7353990798057175728508960092548
                    step 62: 15806891496115451446017931086085
                    + 58068013971064415451169419860851
                    step 63: 73874905467179866897187350946936
                    + 63964905378179866897176450947837
                    step 64: 137839810845359733794363801894773
                    + 377498108363497337953548018938731
                    step 65: 515337919208857071747911820833504
                    + 405338028119747170758802919733515
                    step 66: 920675947328604242506714740567019
                    + 910765047417605242406823749576029
                    step 67: 1831440994746209484913538490143048
                    + 8403410948353194849026474990441381
                    step 68: 10234851943099404333940013480584429
                    + 92448508431004933340499034915843201
                    step 69: 102683360374104337674439048396427630
                    + 036724693840934476733401473063386201
                    step 70: 139408054215038814407840521459813831
                    + 138318954125048704418830512450804931
                    step 71: 277727008340087518826671033910618762
                    + 267816019330176628815780043800727772
                    step 72: 545543027670264147642451077711346534
                    + 435643117770154246741462076720345545
                    step 73: 981186145440418394383913154431692079
                    + 970296134451319383493814044541681189
                    step 74: 1951482279891737777877727198973373268
                    + 8623733798917277787777371989722841591
                    step 75: 10575216078809015565655099188696214859
                    + 95841269688199055656551090887061257501
                    step 76: 106416485767008071222206190075757472360
                    + 063274757570091602222170800767584614601
                    step 77: 169691243337099673444376990843342086961
                    + 169680243348099673444376990733342196961
                    step 78: 339371486685199346888753981576684283922
                    + 229382486675189357888643991586684173933
                    step 79: 568753973360388704777397973163368457855
                    + 558754863361379793777407883063379357865
                    step 80: 1127508836721768498554805856226747815720
                    + 0275187476226585084558948671276388057211
                    step 81: 1402696312948353583113754527503135872931
                    + 1392785313057254573113853538492136962041
                    step 82: 2795481626005608156227608065995272834972
                    + 2794382725995608067226518065006261845972
                    step 83: 5589864352001216223454126131001534680944
                    + 4490864351001316214543226121002534689855
                    step 84: 10080728703002532437997352252004069370799
                    + 99707396040025225379973423520030782708001
                    step 85: 109788124743027757817970775772034852078800
                    + 008870258430277577079718757720347421887901
                    step 86: 118658383173305334897689533492382273966701
                    + 107669372283294335986798433503371383856811
                    step 87: 226327755456599670884487966995753657823512
                    + 215328756357599669784488076995654557723622
                    step 88: 441656511814199340668976043991408215547134
                    + 431745512804199340679866043991418115656144
                    step 89: 873402024618398681348842087982826331203278
                    + 872302133628289780248843186893816420204378
                    step 90: 1745704158246688461597685274876642751407656
                    + 6567041572466784725867951648866428514075471
                    step 91: 8312745730713473187465636923743071265483127
                    + 7213845621703473296365647813743170375472138
                    step 92: 15526591352416946483831284737486241640955265
                    + 56255904614268473748213838464961425319562551
                    step 93: 71782495966685420232045123202447666960517816
                    + 61871506966674420232154023202458666959428717
                    step 94: 133654002933359840464199146404906333919946533
                    + 335649919333609404641991464048953339200456331
                    step 95: 469303922266969245106190610453859673120402864
                    + 468204021376958354016091601542969662229303964
                    step 96: 937507943643927599122282211996829335349706828
                    + 828607943533928699112282221995729346349705739
                    step 97: 1766115887177856298234564433992558681699412567
                    + 7652149961868552993344654328926587717885116671
                    step 98: 9418265849046409291579218762919146399584529238
                    + 8329254859936419192678129751929046409485628149
                    step 99: 17747520708982828484257348514848192809070157387
                    + 78375107090829184841584375248482828980702574771
                    step 100: 96122627799812013325841723763331021789772732158
                    + 85123727798712013336732714852331021899772622169
                    step 101: 181246355598524026662574438615662043689545354327
                    + 723453545986340266516834475266620425895553642181
                    step 102: 904699901584864293179408913882282469585098996508
                    + 805699890585964282288319804971392468485109996409
                    step 103: 1710399792170828575467728718853674938070208992917
                    + 7192998020708394763588178277645758280712979930171
                    step 104: 8903397812879223339055906996499433218783188923088
                    + 8803298813878123349946996095509333229782187933098
                    step 105: 17706696626757346689002903092008766448565376856186
                    + 68165867356584466780029030920098664375762669660771
                    step 106: 85872563983341813469031934012107430824328046516957
                    + 75961564082342803470121043913096431814338936527858
                    step 107: 161834128065684616939152977925203862638666983044815
                    + 518440389666836268302529779251939616486560821438161
                    step 108: 680274517732520885241682757177143479125227804482976
                    + 679284408722521974341771757286142588025237715472086
                    step 109: 1359558926455042859583454514463286067150465519955062
                    + 2605599155640517606823644154543859582405546298559531
                    step 110: 3965158082095560466407098669007145649556011818514593
                    + 3954158181106559465417009668907046640655902808515693
                    step 111: 7919316263202119931824108337914192290211914627030286
                    + 6820307264191120922914197338014281399112023626139197
                    step 112: 14739623527393240854738305675928473689323938253169483
                    + 38496135283932398637482957650383745804239372532693741
                    step 113: 53235758811325639492221263326312219493563310785863224
                    + 42236858701336539491221362336212229493652311885753235
                    step 114: 95472617512662178983442625662524448987215622671616459
                    + 95461617622651278984442526652624438987126621571627459
                    step 115: 190934235135313457967885152315148887974342244243243918
                    + 819342342442243479788841513251588769754313531532439091
                    step 116: 1010276577577556937756726665566737657728655775775683009
                    + 9003865775775568277567376655666276577396557757756720101
                    step 117: 10014142353353125215324103321233014235125213533532403110
                    + 01130423533531252153241033212330142351252135335324141001
                    step 118: 11144565886884377368565136533563156586377348868856544111
                    16002897892 takes 118 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 2,095,962 times since Saturday, March 9th, 2002.)

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