REVERSAL-ADDITION PALINDROME TEST ON 10000505448 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 10000505448: 10000505448 + 84450500001 step 1: 94451005449 + 94450015449 step 2: 188901020898 + 898020109881 step 3: 1086921130779 + 9770311296801 step 4: 10857232427580 + 08572423275801 step 5: 19429655703381 + 18330755692491 step 6: 37760411395872 + 27859311406773 step 7: 65619722802645 + 54620822791656 step 8: 120240545594301 + 103495545042021 step 9: 223736090636322 + 223636090637322 step 10: 447372181273644 + 446372181273744 step 11: 893744362547388 + 883745263447398 step 12: 1777489625994786 + 6874995269847771 step 13: 8652484895842557 + 7552485984842568 step 14: 16204970880685125 + 52158608807940261 step 15: 68363579688625386 + 68352688697536386 step 16: 136716268386161772 + 277161683862617631 step 17: 413877952248779403 + 304977842259778314 step 18: 718855794508557717 + 717755805497558817 step 19: 1436611600006116534 + 4356116000061166341 step 20: 5792727600067282875 + 5782827600067272975 step 21: 11575555200134555850 + 05855543100255557511 step 22: 17431098300390113361 + 16331109300389013471 step 23: 33762207600779126832 + 23862197700670226733 step 24: 57624405301449353565 + 56535394410350442675 step 25: 114159799711799796240 + 042697997117997951411 step 26: 156857796829797747651 + 156747797928697758651 step 27: 313605594758495506302 + 203605594857495506313 step 28: 517211189615991012615 + 516210199516981112715 step 29: 1033421389132972125330 + 0335212792319831243301 step 30: 1368634181452803368631 + 1368633082541814368631 step 31: 2737267263994617737262 + 2627377164993627627372 step 32: 5364644428988245364634 + 4364635428898244464635 step 33: 9729279857886489829269 + 9629289846887589729279 step 34: 19358569704774079558548 + 84585597047740796585391 step 35: 103944166752514876143939 + 939341678415257661449301 step 36: 1043285845167772537593240 + 0423957352777615485823401 step 37: 1467243197945388023416641 + 1466143208835497913427641 step 38: 2933386406780885936844282 + 2824486395880876046833392 step 39: 5757872802661761983677674 + 4767763891671662082787575 step 40: 10525636694333424066465249 + 94256466042433349663652501 step 41: 104782102736766773730117750 + 057711037377667637201287401 step 42: 162493140114434410931405151 + 151504139014434411041394261 step 43: 313997279128868821972799412 + 214997279128868821972799313 step 44: 528994558257737643945598725 + 527895549346737752855499825 step 45: 1056890107604475396801098550 + 0558901086935744067010986501 step 46: 1615791194540219463812085051 + 1505802183649120454911975161 step 47: 3121593378189339918724060212 + 2120604278199339818733951213 step 48: 5242197656388679737458011425 + 5241108547379768836567912425 step 49: 10483306203768448574025923850 + 05832952047584486730260338401 step 50: 16316258251352935304286262251 + 15226268240353925315285261361 step 51: 31542526491706860619571523612 + 21632517591606860719462524513 step 52: 53175044083313721339034048125 + 52184043093312731338044057135 step 53: 105359087176626452677078105260 + 062501870776254626671780953501 step 54: 167860957952881079348859058761 + 167850958843970188259759068761 step 55: 335711916796851267608618127522 + 225721816806762158697619117533 step 56: 561433733603613426306237245055 + 550542732603624316306337334165 step 57: 1111976466207237742612574579220 + 0229754752162477327026646791111 step 58: 1341731218369715069639221370331 + 1330731229369605179638121371431 step 59: 2672462447739320249277342741762 + 2671472437729420239377442642762 step 60: 5343934885468740488654785384524 + 4254835874568840478645884393435 step 61: 9598770760037580967300669777959 + 9597779660037690857300670778959 step 62: 19196550420075271824601340556918 + 81965504310642817257002405569191 step 63: 101162054730718089081603746126109 + 901621647306180980817037450261101 step 64: 1002783702036899069898641196387210 + 0127836911468989609986302073872001 step 65: 1130620613505888679884943270259211 + 1129520723494889768885053160260311 step 66: 2260141337000778448769996430519522 + 2259150346999678448770007331410622 step 67: 4519291684000456897540003761930144 + 4410391673000457986540004861929154 step 68: 8929683357000914884080008623859298 + 8929583268000804884190007533869298 step 69: 17859266625001719768270016157728596 + 69582775161007286791710052666295871 step 70: 87442041786009006559980068824024467 + 76442042886008995560090068714024478 step 71: 163884084672018002120070137538048945 + 549840835731070021200810276480488361 step 72: 713724920403088023320880414018537306 + 603735810414088023320880304029427317 step 73: 1317460730817176046641760718047964623 + 3264697408170671466406717180370647131 step 74: 4582158138987847513048477898418611754 + 4571168148987748403157487898318512854 step 75: 9153326287975595916205965796737124608 + 8064217376975695026195955797826233519 step 76: 17217543664951290942401921594563358127 + 72185336549512910424909215946634571271 step 77: 89402880214464201367311137541197929398 + 89392979114573111376310246441208820498 step 78: 178795859329037312743621383982406749896 + 698947604289383126347213730923958597871 step 79: 877743463618420439090835114906365347767 + 767743563609411538090934024816364347778 step 80: 1645487027227831977181769139722729695545 + 5455969272279319671817791387227207845461 step 81: 7101456299507151648999560526949937541006 + 6001457399496250659998461517059926541017 step 82: 13102913699003402308998022044009864082023 + 32028046890044022089980320430099631920131 step 83: 45130960589047424398978342474109496002154 + 45120069490147424387989342474098506903154 step 84: 90251030079194848786967684948208002905308 + 80350920080284948676968784849197003015209 step 85: 170601950159479797463936469797405005920517 + 715029500504797964639364797974951059106071 step 86: 885631450664277762103301267772356065026588 + 885620560653277762103301267772466054136588 step 87: 1771252011317555524206602535544822119163176 + 6713619112284455352066024255557131102521771 step 88: 8484871123602010876272626791101953221684947 + 7494861223591011976262726780102063211784848 step 89: 15979732347193022852535353571204016433469795 + 59796433461040217535353525822039174323797951 step 90: 75776165808233240387888879393243190757267746 + 64776275709134239397888878304233280856167757 step 91: 140552441517367479785777757697476471613435503 + 305534316174674796757777587974763715144255041 step 92: 446086757692042276543555345672240186757690544 + 445096757681042276543555345672240296757680644 step 93: 891183515373084553087110691344480483515371188 + 881173515384084443196011780355480373515381198 step 94: 1772357030757168996283122471699960857030752386 + 6832570307580699961742213826998617570307532771 step 95: 8604927338337868958025336298698578427338285157 + 7515828337248758968926335208598687338337294068 step 96: 16120755675586627926951671507297265765675579225 + 52297557656756279270517615962972668557655702161 step 97: 68418313332342907197469287470269934323331281386 + 68318213332343996207478296479170924323331381486 step 98: 136736526664686903404947583949440858646662662872 + 278266266646858044949385749404309686466625637631 step 99: 415002793311544948354333333353750545113288300503 + 305003882311545057353333333453849445113397200514 step 100: 720006675623090005707666666807599990226685501017 + 710105586622099995708666666707500090326576600027 step 101: 1430112262245190001416333333515100080553262101044 + 4401012623550800015153333336141000915422622110341 step 102: 5831124885795990016569666669656100995975884211385 10000505448 takes 102 iterations / steps to resolve into a 49 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 2,550,020 times since Saturday, March 9th, 2002.)