REVERSAL-ADDITION PALINDROME TEST ON 15891 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 15891: 15891 + 19851 step 1: 35742 + 24753 step 2: 60495 + 59406 step 3: 119901 + 109911 step 4: 229812 + 218922 step 5: 448734 + 437844 step 6: 886578 + 875688 step 7: 1762266 + 6622671 step 8: 8384937 + 7394838 step 9: 15779775 + 57797751 step 10: 73577526 + 62577537 step 11: 136155063 + 360551631 step 12: 496706694 + 496607694 step 13: 993314388 + 883413399 step 14: 1876727787 + 7877276781 step 15: 9754004568 + 8654004579 step 16: 18408009147 + 74190080481 step 17: 92598089628 + 82698089529 step 18: 175296179157 + 751971692571 step 19: 927267871728 + 827178762729 step 20: 1754446634457 + 7544366444571 step 21: 9298813079028 + 8209703188929 step 22: 17508516267957 + 75976261580571 step 23: 93484777848528 + 82584877748439 step 24: 176069655596967 + 769695556960671 step 25: 945765212557638 + 836755212567549 step 26: 1782520425125187 + 7815215240252871 step 27: 9597735665378058 + 8508735665377959 step 28: 18106471330756017 + 71065703317460181 step 29: 89172174648216198 + 89161284647127198 step 30: 178333459295343396 + 693343592954333871 step 31: 871677052249677267 + 762776942250776178 step 32: 1634453994500453445 + 5443540054993544361 step 33: 7077994049493997806 + 6087993949404997707 step 34: 13165987998898995513 + 31559989889978956131 step 35: 44725977888877951644 + 44615977888877952744 step 36: 89341955777755904388 + 88340955777755914398 step 37: 177682911555511818786 + 687818115555119286771 step 38: 865501027110631105557 + 755501136011720105568 step 39: 1621002163122351211125 + 5211121532213612001261 step 40: 6832123695335963212386 15891 takes 40 iterations / steps to resolve into a 22 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 2,549,922 times since Saturday, March 9th, 2002.)