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.) 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 2,542,363 times since Saturday, March 9th, 2002.)