REVERSAL-ADDITION PALINDROME TEST ON 10309988 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 10309988: 10309988 + 88990301 step 1: 99300289 + 98200399 step 2: 197500688 + 886005791 step 3: 1083506479 + 9746053801 step 4: 10829560280 + 08206592801 step 5: 19036153081 + 18035163091 step 6: 37071316172 + 27161317073 step 7: 64232633245 + 54233623246 step 8: 118466256491 + 194652664811 step 9: 313118921302 + 203129811313 step 10: 516248732615 + 516237842615 step 11: 1032486575230 + 0325756842301 step 12: 1358243417531 + 1357143428531 step 13: 2715386846062 + 2606486835172 step 14: 5321873681234 + 4321863781235 step 15: 9643737462469 + 9642647373469 step 16: 19286384835938 + 83953848368291 step 17: 103240233204229 + 922402332042301 step 18: 1025642565246530 + 0356425652465201 step 19: 1382068217711731 + 1371177128602831 step 20: 2753245346314562 + 2654136435423572 step 21: 5407381781738134 + 4318371871837045 step 22: 9725753653575179 + 9715753563575279 step 23: 19441507217150458 + 85405171270514491 step 24: 104846678487664949 + 949466784876648401 step 25: 1054313463364313350 + 0533134633643134501 step 26: 1587448097007447851 + 1587447007908447851 step 27: 3174895104915895702 + 2075985194015984713 step 28: 5250880298931880415 + 5140881398920880525 step 29: 10391761697852760940 + 04906725879616719301 step 30: 15298487577469480241 + 14208496477578489251 step 31: 29506984055047969492 + 29496974055048960592 step 32: 59003958110096930084 + 48003969001185930095 step 33: 107007927111282860179 + 971068282111729700701 step 34: 1078076209223012560880 + 0880652103229026708701 step 35: 1958728312452039269581 + 1859629302542138278591 step 36: 3818357614994177548172 + 2718457714994167538183 step 37: 6536815329988345086355 + 5536805438899235186356 step 38: 12073620768887580272711 + 11727208578886702637021 step 39: 23800829347774282909732 + 23790928247774392800832 step 40: 47591757595548675710564 + 46501757684559575719574 step 41: 94093515280108251430138 + 83103415280108251539049 step 42: 177196930560216502969187 + 781969205612065039691771 step 43: 959166136172281542660958 + 859066245182271631661959 step 44: 1818232381354553174322917 + 7192234713554531832328181 step 45: 9010467094909085006651098 + 8901566005809094907640109 step 46: 17912033100718179914291207 + 70219241997181700133021971 step 47: 88131275097899880047313178 + 87131374008899879057213188 step 48: 175262649106799759104526366 + 663625401957997601946262571 step 49: 838888051064797361050788937 + 739887050163797460150888838 step 50: 1578775101228594821201677775 + 5777761021284958221015778751 step 51: 7356536122513553042217456526 + 6256547122403553152216356537 step 52: 13613083244917106194433813063 + 36031833449160171944238031631 step 53: 49644916694077278138671844694 + 49644817683187277049661944694 step 54: 99289734377264555188333789388 + 88398733388155546277343798299 step 55: 187688467765420101465677587687 + 786785776564101024567764886781 step 56: 974474244329521126033442474468 + 864474244330621125923442474479 step 57: 1838948488660142251956884948947 + 7498494886591522410668848498381 step 58: 9337443375251664662625733447328 + 8237443375262664661525733447339 step 59: 17574886750514329324151466894667 + 76649866415142392341505768847571 step 60: 94224753165656721665657235742238 + 83224753275656612765656135742249 step 61: 177449506441313334431313371484487 + 784484173313134433313144605944771 step 62: 961933679754447767744457977429258 + 852924779754447767744457976339169 step 63: 1814858459508895535488915953768427 + 7248673595198845355988059548584181 step 64: 9063532054707740891476975502352608 + 8062532055796741980477074502353609 step 65: 17126064110504482871954050004706217 + 71260740005045917828440501146062171 step 66: 88386804115550400700394551150768388 + 88386705115549300700405551140868388 step 67: 176773509231099701400800102291636776 + 677636192201008004107990132905377671 step 68: 854409701432107705508790235197014447 + 744410791532097805507701234107904458 step 69: 1598820492964205511016491469304918905 + 5098194039641946101155024692940288951 step 70: 6697014532606151612171516162245207856 + 6587025422616151712161516062354107966 step 71: 13284039955222303324333032224599315822 + 22851399542223033342330322255993048231 step 72: 36135439497445336666663354480592364053 + 35046329508445336666663354479493453163 step 73: 71181769005890673333326708960085817216 + 61271858006980762333337609850096718117 step 74: 132453627012871435666664318810182535333 + 333535281018813466666534178210726354231 step 75: 465988908031684902333198497020908889564 + 465988809020794891333209486130809889564 step 76: 931977717052479793666407983151718779128 + 821977817151389704666397974250717779139 step 77: 1753955534203869498332805957402436558267 + 7628556342047595082338949683024355593571 step 78: 9382511876251464580671755640426792151838 + 8381512976240465571760854641526781152839 step 79: 17764024852491930152432610281953573304677 + 77640337535918201623425103919425842046771 step 80: 95404362388410131775857714201379415351448 + 84415351497310241775857713101488326340459 step 81: 179819713885720373551715427302867741691907 + 709196147768203724517155373027588317918971 step 82: 889015861653924098068870800330456059610878 + 878016950654033008078860890429356168510988 step 83: 1767032812307957106147731690759812228121866 + 6681218222189570961377416017597032182307671 step 84: 8448251034497528067525147708356844410429537 + 7359240144486538077415257608257944301528448 step 85: 15807491178984066144940405316614788711957985 + 58975911788741661350404944166048987119470851 step 86: 74783402967725727495345349482663775831428836 + 63882413857736628494354359472752776920438747 step 87: 138665816825462355989699708955416552751867583 + 385768157255614559807996989553264528618566831 step 88: 524433974081076915797696698508681081370434414 + 414434073180186805896696797519670180479334425 step 89: 938868047261263721694393496028351261849768839 + 938867948162153820694393496127362162740868839 step 90: 1877735995423417542388786992155713424590637678 + 8767360954243175512996878832457143245995377781 step 91: 10645096949666593055385665824612856670586015459 + 95451068507665821642856658355039566694969054601 step 92: 106096165457332414698242324179652423365555070060 + 060070555563324256971423242896414233754561690601 step 93: 166166721020656671669665567076066657120116760661 + 166067611021756660670765566966176656020127661661 step 94: 332234332042413332340431134042243313140244422322 + 223224442041313342240431134043233314240233432233 step 95: 555458774083726674580862268085476627380477854555 10309988 takes 95 iterations / steps to resolve into a 48 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 2,549,757 times since Saturday, March 9th, 2002.)