REVERSAL-ADDITION PALINDROME TEST ON 18317699990

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 18317699990:
18317699990
+ 09999671381
step 1: 28317371371
+ 17317371382
step 2: 45634742753
+ 35724743654
step 3: 81359486407
+ 70468495318
step 4: 151827981725
+ 527189728151
step 5: 679017709876
+ 678907710976
step 6: 1357925420852
+ 2580245297531
step 7: 3938170718383
+ 3838170718393
step 8: 7776341436776
+ 6776341436777
step 9: 14552682873553
+ 35537828625541
step 10: 50090511499094
+ 49099411509005
step 11: 99189923008099
+ 99080032998199
step 12: 198269956006298
+ 892600659962891
step 13: 1090870615969189
+ 9819695160780901
step 14: 10910565776750090
+ 09005767756501901
step 15: 19916333533251991
+ 19915233533361991
step 16: 39831567066613982
+ 28931666076513893
step 17: 68763233143127875
+ 57872134133236786
step 18: 126635367276364661
+ 166463672763536621
step 19: 293099040039901282
+ 282109930040990392
step 20: 575208970080891674
+ 476198080079802575
step 21: 1051407050160694249
+ 9424960610507041501
step 22: 10476367660667735750
+ 05753776606676367401
step 23: 16230144267344103151
+ 15130144376244103261
step 24: 31360288643588206412
+ 21460288534688206313
step 25: 52820577178276412725
+ 52721467287177502825
step 26: 105542044465453915550
+ 055519354564440245501
step 27: 161061399029894161051
+ 150161498920993160161
step 28: 311222897950887321212
+ 212123788059798222113
step 29: 523346686010685543325
+ 523345586010686643325
step 30: 1046692272021372186650
+ 0566812731202722966401
step 31: 1613505003224095153051
+ 1503515904223005053161
step 32: 3117020907447100206212
+ 2126020017447090207113
step 33: 5243040924894190413325
+ 5233140914984290403425
step 34: 10476181839878480816750
+ 05761808487893818167401
step 35: 16237990327772298984151
+ 15148989227772309973261
step 36: 31386979555544608957412
+ 21475980644555597968313
step 37: 52862960200100206925725
+ 52752960200100206926825
step 38: 105615920400200413852550
+ 055258314002004029516501
step 39: 160874234402204443369051
+ 150963344402204432478061
step 40: 311837578804408875847112
+ 211748578804408875738113
step 41: 523586157608817751585225
+ 522585157718806751685325
step 42: 1046171315327624503270550
+ 0550723054267235131716401
step 43: 1596894369594859634986951
+ 1596894369584959634986951
step 44: 3193788739179819269973902
+ 2093799629189719378873913
step 45: 5287588368369538648847815
+ 5187488468359638638857825
step 46: 10475076836729177287705640
+ 04650778277192763867057401
step 47: 15125855113921941154763041
+ 14036745114912931155852151
step 48: 29162600228834872310615192
+ 29151601327843882200626192
step 49: 58314201556678754511241384
+ 48314211545787665510241385
step 50: 106628413102466420021482769
+ 967284120024664201314826601
step 51: 1073912533127130621336309370
+ 0739036331260317213352193701
step 52: 1812948864387447834688503071
+ 1703058864387447834688492181
step 53: 3516007728774895669376995252
+ 2525996739665984778277006153
step 54: 6042004468440880447654001405
+ 5041004567440880448644002406
step 55: 11083009035881760896298003811
+ 11830089269806718853090038011
step 56: 22913098305688479749388041822
+ 22814088394797488650389031922
step 57: 45727186700485968399777073744
+ 44737077799386958400768172754
step 58: 90464264499872926800545246498
+ 89464254500862927899446246409
step 59: 179928519000735854699991492907
+ 709294199996458537000915829971
step 60: 889222718997194391700907322878
+ 878223709007193491799817222988
step 61: 1767446428004387883500724545866
+ 6685454270053887834008246447671
step 62: 8452900698058275717508970993537
+ 7353990798057175728508960092548
step 63: 15806891496115451446017931086085
+ 58068013971064415451169419860851
step 64: 73874905467179866897187350946936
+ 63964905378179866897176450947837
step 65: 137839810845359733794363801894773
+ 377498108363497337953548018938731
step 66: 515337919208857071747911820833504
+ 405338028119747170758802919733515
step 67: 920675947328604242506714740567019
+ 910765047417605242406823749576029
step 68: 1831440994746209484913538490143048
+ 8403410948353194849026474990441381
step 69: 10234851943099404333940013480584429
+ 92448508431004933340499034915843201
step 70: 102683360374104337674439048396427630
+ 036724693840934476733401473063386201
step 71: 139408054215038814407840521459813831
+ 138318954125048704418830512450804931
step 72: 277727008340087518826671033910618762
+ 267816019330176628815780043800727772
step 73: 545543027670264147642451077711346534
+ 435643117770154246741462076720345545
step 74: 981186145440418394383913154431692079
+ 970296134451319383493814044541681189
step 75: 1951482279891737777877727198973373268
+ 8623733798917277787777371989722841591
step 76: 10575216078809015565655099188696214859
+ 95841269688199055656551090887061257501
step 77: 106416485767008071222206190075757472360
+ 063274757570091602222170800767584614601
step 78: 169691243337099673444376990843342086961
+ 169680243348099673444376990733342196961
step 79: 339371486685199346888753981576684283922
+ 229382486675189357888643991586684173933
step 80: 568753973360388704777397973163368457855
+ 558754863361379793777407883063379357865
step 81: 1127508836721768498554805856226747815720
+ 0275187476226585084558948671276388057211
step 82: 1402696312948353583113754527503135872931
+ 1392785313057254573113853538492136962041
step 83: 2795481626005608156227608065995272834972
+ 2794382725995608067226518065006261845972
step 84: 5589864352001216223454126131001534680944
+ 4490864351001316214543226121002534689855
step 85: 10080728703002532437997352252004069370799
+ 99707396040025225379973423520030782708001
step 86: 109788124743027757817970775772034852078800
+ 008870258430277577079718757720347421887901
step 87: 118658383173305334897689533492382273966701
+ 107669372283294335986798433503371383856811
step 88: 226327755456599670884487966995753657823512
+ 215328756357599669784488076995654557723622
step 89: 441656511814199340668976043991408215547134
+ 431745512804199340679866043991418115656144
step 90: 873402024618398681348842087982826331203278
+ 872302133628289780248843186893816420204378
step 91: 1745704158246688461597685274876642751407656
+ 6567041572466784725867951648866428514075471
step 92: 8312745730713473187465636923743071265483127
+ 7213845621703473296365647813743170375472138
step 93: 15526591352416946483831284737486241640955265
+ 56255904614268473748213838464961425319562551
step 94: 71782495966685420232045123202447666960517816
+ 61871506966674420232154023202458666959428717
step 95: 133654002933359840464199146404906333919946533
+ 335649919333609404641991464048953339200456331
step 96: 469303922266969245106190610453859673120402864
+ 468204021376958354016091601542969662229303964
step 97: 937507943643927599122282211996829335349706828
+ 828607943533928699112282221995729346349705739
step 98: 1766115887177856298234564433992558681699412567
+ 7652149961868552993344654328926587717885116671
step 99: 9418265849046409291579218762919146399584529238
+ 8329254859936419192678129751929046409485628149
step 100: 17747520708982828484257348514848192809070157387
+ 78375107090829184841584375248482828980702574771
step 101: 96122627799812013325841723763331021789772732158
+ 85123727798712013336732714852331021899772622169
step 102: 181246355598524026662574438615662043689545354327
+ 723453545986340266516834475266620425895553642181
step 103: 904699901584864293179408913882282469585098996508
+ 805699890585964282288319804971392468485109996409
step 104: 1710399792170828575467728718853674938070208992917
+ 7192998020708394763588178277645758280712979930171
step 105: 8903397812879223339055906996499433218783188923088
+ 8803298813878123349946996095509333229782187933098
step 106: 17706696626757346689002903092008766448565376856186
+ 68165867356584466780029030920098664375762669660771
step 107: 85872563983341813469031934012107430824328046516957
+ 75961564082342803470121043913096431814338936527858
step 108: 161834128065684616939152977925203862638666983044815
+ 518440389666836268302529779251939616486560821438161
step 109: 680274517732520885241682757177143479125227804482976
+ 679284408722521974341771757286142588025237715472086
step 110: 1359558926455042859583454514463286067150465519955062
+ 2605599155640517606823644154543859582405546298559531
step 111: 3965158082095560466407098669007145649556011818514593
+ 3954158181106559465417009668907046640655902808515693
step 112: 7919316263202119931824108337914192290211914627030286
+ 6820307264191120922914197338014281399112023626139197
step 113: 14739623527393240854738305675928473689323938253169483
+ 38496135283932398637482957650383745804239372532693741
step 114: 53235758811325639492221263326312219493563310785863224
+ 42236858701336539491221362336212229493652311885753235
step 115: 95472617512662178983442625662524448987215622671616459
+ 95461617622651278984442526652624438987126621571627459
step 116: 190934235135313457967885152315148887974342244243243918
+ 819342342442243479788841513251588769754313531532439091
step 117: 1010276577577556937756726665566737657728655775775683009
+ 9003865775775568277567376655666276577396557757756720101
step 118: 10014142353353125215324103321233014235125213533532403110
+ 01130423533531252153241033212330142351252135335324141001
step 119: 11144565886884377368565136533563156586377348868856544111
18317699990 takes 119 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 1,734,338 times since Saturday, March 9th, 2002.)