REVERSAL-ADDITION PALINDROME TEST ON 800067199 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 800067199: 800067199 + 991760008 step 1: 1791827207 + 7027281971 step 2: 8819109178 + 8719019188 step 3: 17538128366 + 66382183571 step 4: 83920311937 + 73911302938 step 5: 157831614875 + 578416138751 step 6: 736247753626 + 626357742637 step 7: 1362605496263 + 3626945062631 step 8: 4989550558894 + 4988550559894 step 9: 9978101118788 + 8878111018799 step 10: 18856212137587 + 78573121265881 step 11: 97429333403468 + 86430433392479 step 12: 183859766795947 + 749597667958381 step 13: 933457434754328 + 823457434754339 step 14: 1756914869508667 + 7668059684196571 step 15: 9424974553705238 + 8325073554794249 step 16: 17750048108499487 + 78499480184005771 step 17: 96249528292505258 + 85250529282594269 step 18: 181500057575099527 + 725990575750005181 step 19: 907490633325104708 + 807401523336094709 step 20: 1714892156661199417 + 7149911666512984171 step 21: 8864803823174183588 + 8853814713283084688 step 22: 17718618536457268276 + 67286275463581681771 step 23: 85004894000038950047 + 74005983000049840058 step 24: 159010877000088790105 + 501097880000778010951 step 25: 660108757000866801056 + 650108668000757801066 step 26: 1310217425001624602122 + 2212064261005247120131 step 27: 3522281686006871722253 + 3522271786006861822253 step 28: 7044553472013733544506 + 6054453373102743554407 step 29: 13099006845116477098913 + 31989077461154860099031 step 30: 45088084306271337197944 + 44979173317260348088054 step 31: 90067257623531685285998 + 89958258613532675276009 step 32: 180025516237064360562007 + 700265063460732615520081 step 33: 880290579697796976082088 + 880280679697796975092088 step 34: 1760571259395593951174176 + 6714711593955939521750671 step 35: 8475282853351533472924847 + 7484292743351533582825748 step 36: 15959575596703067055750595 + 59505755076030769557595951 step 37: 75465330672733836613346546 + 64564331663833727603356457 step 38: 140029662336567564216703003 + 300307612465765633266920041 step 39: 440337274802333197483623044 + 440326384791333208472733044 step 40: 880663659593666405956356088 + 880653659504666395956366088 step 41: 1761317319098332801912722176 + 6712272191082338909137131671 step 42: 8473589510180671711049853847 + 7483589401171760810159853748 step 43: 15957178911352432521209707595 + 59570790212523425311987175951 step 44: 75527969123875857833196883546 + 64538869133875857832196972557 step 45: 140066838257751715665393856103 + 301658393566517157752838660041 step 46: 441725231824268873418232516144 + 441615232814378862428132527144 step 47: 883340464638647735846365043288 + 882340563648537746836464043388 step 48: 1765681028287185482682829086676 + 6766809282862845817828201865671 step 49: 8532490311150031300511030952347 + 7432590301150031300511130942358 step 50: 15965080612300062601022161894705 + 50749816122010626000321608056951 step 51: 66714896734310688601343769951656 + 65615996734310688601343769841766 step 52: 132330893468621377202687539793422 + 224397935786202773126864398033231 step 53: 356728829254824150329551937826653 + 356628739155923051428452928827653 step 54: 713357568410747201758004866654306 + 603456668400857102747014865753317 step 55: 1316814236811604304505019732407623 + 3267042379105054034061186324186131 step 56: 4583856615916658338566206056593754 + 4573956506026658338566195166583854 step 57: 9157813121943316677132401223177608 + 8067713221042317766133491213187519 step 58: 17225526342985634443265892436365127 + 72156363429856234443658924362552271 step 59: 89381889772841868886924816798917398 + 89371989761842968886814827798818398 step 60: 178753879534684837773739644597735796 + 697537795446937377738486435978357871 step 61: 876291674981622215512226080576093667 + 766390675080622215512226189476192678 step 62: 1642682350062244431024452270052286345 + 5436822500722544201344422600532862461 step 63: 7079504850784788632368874870585148806 + 6088415850784788632368874870584059707 step 64: 13167920701569577264737749741169208513 + 31580296114794773746277596510702976131 step 65: 44748216816364351011015346251872184644 + 44648127815264351011015346361861284744 step 66: 89396344631628702022030692613733469388 + 88396433731629603022020782613644369398 step 67: 177792778363258305044051475227377838786 + 687838773722574150440503852363877297771 step 68: 865631552085832455484555327591255136557 + 755631552195723555484554238580255136568 step 69: 1621263104281556010969109566171510273125 + 5213720151716659019690106551824013621261 step 70: 6834983255998215030659216117995523894386 + 6834983255997116129560305128995523894386 step 71: 13669966511995331160219521246991047788772 + 27788774019964212591206113359911566996631 step 72: 41458740531959543751425634606902614785403 + 30458741620960643652415734595913504785414 step 73: 71917482152920187403841369202816119570817 + 71807591161820296314830478102925128471917 step 74: 143725073314740483718671847305741248042734 + 437240842147503748176817384047413370527341 step 75: 580965915462244231895489231353154618570075 + 570075816451353132984598132442264519569085 step 76: 1151041731913597364880087363795419138139160 + 0619318319145973637800884637953191371401511 step 77: 1770360051059571002680972001748610509540671 + 1760459050168471002790862001759501500630771 step 78: 3530819101228042005471834003508112010171442 + 2441710102118053004381745002408221019180353 step 79: 5972529203346095009853579005916333029351795 + 5971539203336195009753589005906433029252795 step 80: 11944068406682290019607168011822766058604590 + 09540685066722811086170691009228660486044911 step 81: 21484753473405101105777859021051426544649501 + 10594644562415012095877750110150437435748412 step 82: 32079398035820113201655609131201863980397913 + 31979308936810213190655610231102853089397023 step 83: 64058706972630326392311219362304717069794936 + 63949796071740326391211329362303627960785046 step 84: 128008503044370652783522548724608345030579982 + 289975030543806427845225387256073440305800821 step 85: 417983533588177080628747935980681785336380803 + 308083633587186089539747826080771885335389714 step 86: 726067167175363170168495762061453670671770517 + 715077176076354160267594861071363571761760627 step 87: 1441144343251717330436090623132817242433531144 + 4411353342427182313260906340337171523434411441 step 88: 5852497685678899643696996963469988765867942585 800067199 takes 88 iterations / steps to resolve into a 46 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 2,550,047 times since Saturday, March 9th, 2002.)