REVERSAL-ADDITION PALINDROME TEST ON 100900509906 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 100900509906: 100900509906 + 609905009001 step 1: 710805518907 + 709815508017 step 2: 1420621026924 + 4296201260241 step 3: 5716822287165 + 5617822286175 step 4: 11334644573340 + 04337544643311 step 5: 15672189216651 + 15661298127651 step 6: 31333487344302 + 20344378433313 step 7: 51677865777615 + 51677756877615 step 8: 103355622655230 + 032556226553301 step 9: 135911849208531 + 135802948119531 step 10: 271714797328062 + 260823797417172 step 11: 532538594745234 + 432547495835235 step 12: 965086090580469 + 964085090680569 step 13: 1929171181261038 + 8301621811719291 step 14: 10230792992980329 + 92308929929703201 step 15: 102539722922683530 + 035386229227935201 step 16: 137925952150618731 + 137816051259529731 step 17: 275742003410148462 + 264841014300247572 step 18: 540583017710396034 + 430693017710385045 step 19: 971276035420781079 + 970187024530672179 step 20: 1941463059951453258 + 8523541599503641491 step 21: 10465004659455094749 + 94749055495640056401 step 22: 105214060155095151150 + 051151590551060412501 step 23: 156365650706155563651 + 156365551607056563651 step 24: 312731202313212127302 + 203721212313202137213 step 25: 516452414626414264515 + 515462414626414254615 step 26: 1031914829252828519130 + 0319158282529284191301 step 27: 1351073111782112710431 + 1340172112871113701531 step 28: 2691245224653226411962 + 2691146223564225421962 step 29: 5382391448217451833924 + 4293381547128441932835 step 30: 9675772995345893766759 + 9576673985435992775769 step 31: 19252446980781886542528 + 82524568818708964425291 step 32: 101777015799490850967819 + 918769058094997510777101 step 33: 1020546073894488361744920 + 0294471638844983706450201 step 34: 1315017712739472068195121 + 1215918602749372177105131 step 35: 2530936315488844245300252 + 2520035424488845136390352 step 36: 5050971739977689381690604 + 4060961839867799371790505 step 37: 9111933579845488753481109 + 9011843578845489753391119 step 38: 18123777158690978506872228 + 82227860587909685177732181 step 39: 100351637746600663684604409 + 904406486366006647736153001 step 40: 1004758124112607311420757410 + 0147570241137062114218574001 step 41: 1152328365249669425639331411 + 1141339365249669425638232511 step 42: 2293667730499338851277563922 + 2293657721588339940377663922 step 43: 4587325452087678791655227844 + 4487225561978767802545237854 step 44: 9074551014066446594200465698 + 8965640024956446604101554709 step 45: 18040191039022893198302020407 + 70402020389139822093019104081 step 46: 88442211428162715291321124488 + 88442112319251726182411224488 step 47: 176884323747414441473732348976 + 679843237374144414747323488671 step 48: 856727561121558856221055837647 + 746738550122658855121165727658 step 49: 1603466111244217711342221565305 + 5035651222431177124421116643061 step 50: 6639117333675394835763338208366 + 6638028333675384935763337119366 step 51: 13277145667350779771526675327732 + 23772357662517797705376654177231 step 52: 37049503329868577476903329504963 + 36940592330967477586892330594073 step 53: 73990095660836055063795660099036 + 63099006659736055063806659009937 step 54: 137089102320572110127602319108973 + 379801913206721011275023201980731 step 55: 516891015527293121402625521089704 + 407980125526204121392725510198615 step 56: 924871141053497242795351031288319 + 913882130153597242794350141178429 step 57: 1838753271207094485589701172466748 + 8476642711079855844907021723578381 step 58: 10315395982286950330496722896045129 + 92154069822769403305968228959351301 step 59: 102469465805056353636464951855396430 + 034693558159464636353650508564964201 step 60: 137163023964520989990115460420360631 + 136063024064511099989025469320361731 step 61: 273226048029032089979140929740722362 + 263227047929041979980230920840622372 step 62: 536453095958074069959371850581344734 + 437443185058173959960470859590354635 step 63: 973896281016248029919842710171699369 + 963996171017248919920842610182698379 step 64: 1937892452033496949840685320354397748 + 8477934530235860489496943302542987391 step 65: 10415826982269357439337628622897385139 + 93158379822682673393475396228962851401 step 66: 103574206804952030832813024851860236540 + 045632068158420318238030259408602475301 step 67: 149206274963372349070843284260462711841 + 148117264062482348070943273369472602941 step 68: 297323539025854697141786557629935314782 + 287413539926755687141796458520935323792 step 69: 584737078952610384283583016150870638574 + 475836078051610385382483016259870737485 step 70: 1060573157004220769666066032410741376059 + 9506731470142306606669670224007513750601 step 71: 10567304627146527376335736256418255126660 + 06662155281465263753367372564172640376501 step 72: 17229459908611791129703108820590895503161 + 16130559809502880130792119711680995492271 step 73: 33360019718114671260495228532271890995432 + 23459909817223582259406217641181791006333 step 74: 56819929535338253519901446173453682001765 + 56710028635437164410991535283353592991865 step 75: 113529958170775417930892981456807274993630 + 036399472708654189298039714577071859925311 step 76: 149929430879429607228932696033879134918941 + 149819431978330696239822706924978034929941 step 77: 299748862857760303468755402958857169848882 + 288848961758859204557864303067758268847992 step 78: 588597824616619508026619706026615438696874 + 478696834516620607916620805916616428795885 step 79: 1067294659133240115943240511943231867492759 + 9572947681323491150423495110423319564927601 step 80: 10640242340456731266366735622366551432420360 + 06302423415566322653766366213765404324204601 step 81: 16942665756023053920133101836131955756624961 + 16942665755913163810133102935032065756624961 step 82: 33885331511936217730266204771164021513249922 + 22994231512046117740266203771263911513358833 step 83: 56879563023982335470532408542427933026608755 + 55780662033972424580423507453328932036597865 step 84: 112660225057954760050955915995756865063206620 + 026602360568657599519559050067459750522066211 step 85: 139262585626612359570514966063216615585272831 + 138272585516612360669415075953216626585262931 step 86: 277535171143224720239930042016433242170535762 + 267535071242334610240039932027422341171535772 step 87: 545070242385559330479969974043855583342071534 + 435170243385558340479969974033955583242070545 step 88: 980240485771117670959939948077811166584142079 + 970241485661118770849939959076711177584042089 step 89: 1950481971432236441809879907154522344168184168 + 8614818614432254517099789081446322341791840591 step 90: 10565300585864490958909668988600844685960024759 + 95742006958644800688986690985909446858500356501 step 91: 106307307544509291647896359974510291544460381260 + 062183064445192015479953698746192905445703703601 step 92: 168490371989701307127850058720703196990164084861 + 168480461099691307027850058721703107989173094861 step 93: 336970833089392614155700117442406304979337179722 + 227971733979403604244711007551416293980338079633 step 94: 564942567068796218400411124993822598959675259355 + 553952576959895228399421114004812697860765249465 step 95: 1118895144028691446799832238998635296820440508820 + 0288050440286925368998322389976441968204415988111 step 96: 1406945584315616815798154628975077265024856496931 + 1396946584205627705798264518975186165134855496041 step 97: 2803892168521244521596419147950263430159711992972 + 2792991179510343620597419146951254421258612983082 step 98: 5596883348031588142193838294901517851418324976054 + 4506794238141587151094928383912418851308433886955 step 99: 10103677586173175293288766678813936702726758863009 + 90036885762720763931887666788239257137168577630101 step 100: 100140563348893939225176433467053193839895336493110 + 011394633598938391350764334671522939398843365041001 step 101: 111535196947832330575940768138576133238738701534111 + 111435107837832331675831867049575033238749691535111 step 102: 222970304785664662251772635188151166477488393069222 + 222960393884774661151881536277152266466587403079222 step 103: 445930698670439323403654171465303432944075796148444 + 444841697570449234303564171456304323934076896039544 step 104: 890772396240888557707218342921607756878152692187988 + 889781296251878657706129243812707755888042693277098 step 105: 1780553692492767215413347586734315512766195385465086 + 6805645835916672155134376857433145127672942963550871 step 106: 8586199528409439370547724444167460640439138349015957 + 7595109438319340460647614444277450739349048259916858 step 107: 16181308966728779831195338888444911379788186608932815 + 51823980668188797311944488883359113897782766980318161 step 108: 68005289634917577143139827771804025277570953589250976 + 67905298535907577252040817772893134177571943698250086 step 109: 135910588170825154395180645544697159455142897287501062 + 260105782798241554951796445546081593451528071885019531 step 110: 396016370969066709346977091090778752906670969172520593 + 395025271969076609257877090190779643907660969073610693 step 111: 791041642938143318604854181281558396814331938246131286 + 682131642839133418693855182181458406813341839246140197 step 112: 1473173285777276737298709363463016803627673777492271483 + 3841722947773767263086103643639078927376727775823713741 step 113: 5314896233551044000384813007102095731004401553315985224 + 4225895133551044001375902017003184830004401553326984135 step 114: 9540791367102088001760715024105280561008803106642969359 + 9539692466013088001650825014205170671008802017631970459 step 115: 19080483833115176003411540038310451232017605124274939818 + 81893947242150671023215401383004511430067151133838408091 step 116: 100974431075265847026626941421314962662084756258113347909 + 909743311852657480266269413124149626620748562570134479001 step 117: 1010717742927923327292896354545464589282833318828247826910 + 0196287428288133382829854645454536982927233297292477170101 step 118: 1207005171216056710122751000000001572210066616120724997011 + 1107994270216166600122751000000001572210176506121715007021 step 119: 2314999441432223310245502000000003144420243122242440004032 + 2304000442422213420244413000000002055420133222341449994132 step 120: 4618999883854436730489915000000005199840376344583889998164 100900509906 takes 120 iterations / steps to resolve into a 58 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 2,542,530 times since Saturday, March 9th, 2002.)