REVERSAL-ADDITION PALINDROME TEST ON 10548 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 10548: 10548 + 84501 step 1: 95049 + 94059 step 2: 189108 + 801981 step 3: 991089 + 980199 step 4: 1971288 + 8821791 step 5: 10793079 + 97039701 step 6: 107832780 + 087238701 step 7: 195071481 + 184170591 step 8: 379242072 + 270242973 step 9: 649485045 + 540584946 step 10: 1190069991 + 1999600911 step 11: 3189670902 + 2090769813 step 12: 5280440715 + 5170440825 step 13: 10450881540 + 04518805401 step 14: 14969686941 + 14968696941 step 15: 29938383882 + 28838383992 step 16: 58776767874 + 47876767785 step 17: 106653535659 + 956535356601 step 18: 1063188892260 + 0622988813601 step 19: 1686177705861 + 1685077716861 step 20: 3371255422722 + 2272245521733 step 21: 5643500944455 + 5544490053465 step 22: 11187990997920 + 02979909978111 step 23: 14167900976031 + 13067900976141 step 24: 27235801952172 + 27125910853272 step 25: 54361712805444 + 44450821716345 step 26: 98812534521789 + 98712543521889 step 27: 197525078043678 + 876340870525791 step 28: 1073865948569469 + 9649658495683701 step 29: 10723524444253170 + 07135244442532701 step 30: 17858768886785871 10548 takes 30 iterations / steps to resolve into a 17 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 2,542,536 times since Saturday, March 9th, 2002.)