REVERSAL-ADDITION PALINDROME TEST ON 131996 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 131996: 131996 + 699131 step 1: 831127 + 721138 step 2: 1552265 + 5622551 step 3: 7174816 + 6184717 step 4: 13359533 + 33595331 step 5: 46954864 + 46845964 step 6: 93800828 + 82800839 step 7: 176601667 + 766106671 step 8: 942708338 + 833807249 step 9: 1776515587 + 7855156771 step 10: 9631672358 + 8532761369 step 11: 18164433727 + 72733446181 step 12: 90897879908 + 80997879809 step 13: 171895759717 + 717957598171 step 14: 889853357888 + 888753358988 step 15: 1778606716876 + 6786176068771 step 16: 8564782785647 + 7465872874658 step 17: 16030655660305 + 50306655603061 step 18: 66337311263366 + 66336211373366 step 19: 132673522636732 + 237636225376231 step 20: 370309748012963 + 369210847903073 step 21: 739520595916036 + 630619595025937 step 22: 1370140190941973 + 3791490910410731 step 23: 5161631101352704 + 4072531011361615 step 24: 9234162112714319 + 9134172112614329 step 25: 18368334225328648 + 84682352243386381 step 26: 103050686468715029 + 920517864686050301 step 27: 1023568551154765330 + 0335674511558653201 step 28: 1359243062713418531 + 1358143172603429531 step 29: 2717386235316848062 + 2608486135326837172 step 30: 5325872370643685234 + 4325863460732785235 step 31: 9651735831376470469 + 9640746731385371569 step 32: 19292482562761842038 + 83024816726528429291 step 33: 102317299289290271329 + 923172092982992713201 step 34: 1025489392272282984530 + 0354892822722939845201 step 35: 1380382214995222829731 + 1379282225994122830831 step 36: 2759664440989345660562 + 2650665439890444669572 step 37: 5410329880879790330134 + 4310330979780889230145 step 38: 9720660860660679560279 + 9720659760660680660279 step 39: 19441320621321360220558 + 85502206312312602314491 step 40: 104943526933633962535049 + 940535269336339625349401 step 41: 1045478796269973587884450 + 0544887853799626978745401 step 42: 1590366650069600566629851 + 1589266650069600566630951 step 43: 3179633300139201133260802 + 2080623311029310033369713 step 44: 5260256611168511166630515 + 5150366611158611166520625 step 45: 10410623222327122333151140 + 04115133322172322232601401 step 46: 14525756544499444565752541 131996 takes 46 iterations / steps to resolve into a 26 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 2,499,129 times since Saturday, March 9th, 2002.)