REVERSAL-ADDITION PALINDROME TEST ON 1058921 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 1058921: 1058921 + 1298501 step 1: 2357422 + 2247532 step 2: 4604954 + 4594064 step 3: 9199018 + 8109919 step 4: 17308937 + 73980371 step 5: 91289308 + 80398219 step 6: 171687527 + 725786171 step 7: 897473698 + 896374798 step 8: 1793848496 + 6948483971 step 9: 8742332467 + 7642332478 step 10: 16384664945 + 54946648361 step 11: 71331313306 + 60331313317 step 12: 131662626623 + 326626266131 step 13: 458288892754 + 457298882854 step 14: 915587775608 + 806577785519 step 15: 1722165561127 + 7211655612271 step 16: 8933821173398 + 8933711283398 step 17: 17867532456796 + 69765423576871 step 18: 87632956033667 + 76633065923678 step 19: 164266021957345 + 543759120662461 step 20: 708025142619806 + 608916241520807 step 21: 1316941384140613 + 3160414831496131 step 22: 4477356215636744 + 4476365126537744 step 23: 8953721342174488 + 8844712431273598 step 24: 17798433773448086 + 68084437733489771 step 25: 85882871506937857 + 75873960517828858 step 26: 161756832024766715 + 517667420238657161 step 27: 679424252263423876 + 678324362252424976 step 28: 1357748614515848852 + 2588485154168477531 step 29: 3946233768684326383 + 3836234868673326493 step 30: 7782468637357652876 + 6782567537368642877 step 31: 14565036174726295753 + 35759262747163056541 step 32: 50324298921889352294 + 49225398812989242305 step 33: 99549697734878594599 + 99549587843779694599 step 34: 199099285578658289198 + 891982856875582990991 step 35: 1091082142454241280189 + 9810821424542412801901 step 36: 10901903566996654082090 + 09028045669966530910901 step 37: 19929949236963184992991 + 19929948136963294992991 step 38: 39859897373926479985982 + 28958997462937379895893 step 39: 68818894836863859881875 + 57818895836863849881886 step 40: 126637790673727709763761 + 167367907727376097736621 step 41: 294005698401103807500382 + 283005708301104896500492 step 42: 577011406702208704000874 + 478000407802207604110775 step 43: 1055011814504416308111649 + 9461118036144054181105501 step 44: 10516129850648470489217150 + 05171298407484605892161501 step 45: 15687428258133076381378651 + 15687318367033185282478651 step 46: 31374746625166261663857302 + 20375836616266152664747313 step 47: 51750583241432414328604615 + 51640682341423414238505715 step 48: 103391265582855828567110330 + 033011765828558285562193301 step 49: 136403031411414114129303631 + 136303921411414114130304631 step 50: 272706952822828228259608262 + 262806952822828228259607272 step 51: 535513905645656456519215534 + 435512915654656546509315535 step 52: 971026821300313003028531069 + 960135820300313003128620179 step 53: 1931162641600626006157151248 + 8421517516006260061462611391 step 54: 10352680157606886067619762639 + 93626791676068860675108625301 step 55: 103979471833675746742728387940 + 049783827247647576338174979301 step 56: 153763299081323323080903367241 + 142763309080323323180992367351 step 57: 296526608161646646261895734592 + 295437598162646646161806625692 step 58: 591964206324293292423702360284 + 482063207324292392423602469195 step 59: 1074027413648585684847304829479 + 9749284037484865858463147204701 step 60: 10823311451133451543310452034180 + 08143025401334515433115411332801 step 61: 18966336852467966976425863366981 1058921 takes 61 iterations / steps to resolve into a 32 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 2,549,997 times since Saturday, March 9th, 2002.)