REVERSAL-ADDITION PALINDROME TEST ON 100055896 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 100055896: 100055896 + 698550001 step 1: 798605897 + 798506897 step 2: 1597112794 + 4972117951 step 3: 6569230745 + 5470329656 step 4: 12039560401 + 10406593021 step 5: 22446153422 + 22435164422 step 6: 44881317844 + 44871318844 step 7: 89752636688 + 88663625798 step 8: 178416262486 + 684262614871 step 9: 862678877357 + 753778876268 step 10: 1616457753625 + 5263577546161 step 11: 6880035299786 + 6879925300886 step 12: 13759960600672 + 27600606995731 step 13: 41360567596403 + 30469576506314 step 14: 71830144102717 + 71720144103817 step 15: 143550288206534 + 435602882055341 step 16: 579153170261875 + 578162071351975 step 17: 1157315241613850 + 0583161425137511 step 18: 1740476666751361 + 1631576666740471 step 19: 3372053333491832 + 2381943333502733 step 20: 5753996666994565 + 5654996666993575 step 21: 11408993333988140 + 04188933339980411 step 22: 15597926673968551 + 15586937662979551 step 23: 31184864336948102 + 20184963346848113 step 24: 51369827683796215 + 51269738672896315 step 25: 102639566356692530 + 035296653665936201 step 26: 137936220022628731 + 137826220022639731 step 27: 275762440045268462 + 264862540044267572 step 28: 540624980089536034 + 430635980089426045 step 29: 971260960178962079 + 970269871069062179 step 30: 1941530831248024258 + 8524208421380351491 step 31: 10465739252628375749 + 94757382625293756401 step 32: 105223121877922132150 + 051231229778121322501 step 33: 156454351656043454651 + 156454340656153454651 step 34: 312908692312196909302 + 203909691213296809213 step 35: 516818383525493718515 + 515817394525383818615 step 36: 1032635778050877537130 + 0317357780508775362301 step 37: 1349993558559652899431 + 1349982569558553999431 step 38: 2699976128118206898862 + 2688986028118216799962 step 39: 5388962156236423698824 + 4288963246326512698835 step 40: 9677925402562936397659 + 9567936392652045297769 step 41: 19245861795214981695428 + 82459618941259716854291 step 42: 101705480736474698549719 + 917945896474637084507101 step 43: 1019651377211111783056820 + 0286503871111127731569101 step 44: 1306155248322239514625921 + 1295264159322238425516031 step 45: 2601419407644477940141952 + 2591410497744467049141062 step 46: 5192829905388944989283014 + 4103829894498835099282915 step 47: 9296659799887780088565929 + 9295658800877889979566929 step 48: 18592318600765670068132858 + 85823186007656700681329581 step 49: 104415504608422370749462439 + 934264947073224806405514401 step 50: 1038680451681647177154976840 + 0486794517717461861540868301 step 51: 1525474969399109038695845141 + 1415485968309019939694745251 step 52: 2940960937708128978390590392 + 2930950938798218077390690492 step 53: 5871911876506347055781280884 + 4880821875507436056781191785 step 54: 10752733752013783112562472669 + 96627426521138731025733725701 step 55: 107380160273152514138296198370 + 073891692831415251372061083701 step 56: 181271853104567765510357282071 + 170282753015567765401358172181 step 57: 351554606120135530911715454252 + 252454517119035531021606455153 step 58: 604009123239171061933321909405 + 504909123339160171932321900406 step 59: 1108918246578331233865643809811 + 1189083465683321338756428198011 step 60: 2298001712261652572622072007822 + 2287002702262752561622171008922 step 61: 4585004414524405134244243016744 + 4476103424424315044254144005854 step 62: 9061107838948720178498387022598 + 8952207838948710278498387011609 step 63: 18013315677897430456996774034207 + 70243047769965403479877651331081 step 64: 88256363447862833936874425365288 + 88256352447863933826874436365288 step 65: 176512715895726767763748861730576 + 675037168847367767627598517215671 step 66: 851549884743094535391347378946247 + 742649873743193535490347488945158 step 67: 1594199758486288070881694867891405 + 5041987684961880708826848579914951 step 68: 6636187443448168779708543447806356 + 6536087443458079778618443447816366 step 69: 13172274886906248558326986895622722 + 22722659868962385584260968847227131 step 70: 35894934755868634142587955742849853 + 35894824755978524143686855743949853 step 71: 71789759511847158286274811486799706 + 60799768411847268285174811595798717 step 72: 132589527923694426571449623082598423 + 324895280326944175624496329725985231 step 73: 457484808250638602195945952808583654 + 456385808259549591206836052808484754 step 74: 913870616510188193402782005617068408 + 804860716500287204391881015616078319 step 75: 1718731333010475397794663021233146727 + 7276413321203664977935740103331378171 step 76: 8995144654214140375730403124564524898 + 8984254654213040375730414124564415998 step 77: 17979399308427180751460817249128940896 + 69804982194271806415708172480399397971 step 78: 87784381502698987167168989729528338867 + 76883382592798986176178989620518348778 step 79: 164667764095497973343347979350046687645 + 546786640053979743343379794590467766461 step 80: 711454404149477716686727773940514454106 + 601454415049377727686617774941404454117 step 81: 1312908819198855444373345548881918908223 + 3228098191888455433734445588919188092131 step 82: 4541007011087310878107791137801107000354 + 4530007011087311977018780137801107001454 step 83: 9071014022174622855126571275602214001808 + 8081004122065721756215582264712204101709 step 84: 17152018144240344611342153540314418103517 + 71530181441304535124311644304244181025171 step 85: 88682199585544879735653797844558599128688 100055896 takes 85 iterations / steps to resolve into a 41 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 2,542,356 times since Saturday, March 9th, 2002.)