REVERSAL-ADDITION PALINDROME TEST ON 13697 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 13697: 13697 + 79631 step 1: 93328 + 82339 step 2: 175667 + 766571 step 3: 942238 + 832249 step 4: 1774487 + 7844771 step 5: 9619258 + 8529169 step 6: 18148427 + 72484181 step 7: 90632608 + 80623609 step 8: 171256217 + 712652171 step 9: 883908388 + 883809388 step 10: 1767717776 + 6777177671 step 11: 8544895447 + 7445984458 step 12: 15990879905 + 50997809951 step 13: 66988689856 + 65898688966 step 14: 132887378822 + 228873788231 step 15: 361761167053 + 350761167163 step 16: 712522334216 + 612433225217 step 17: 1324955559433 + 3349555594231 step 18: 4674511153664 + 4663511154764 step 19: 9338022308428 + 8248032208339 step 20: 17586054516767 + 76761545068571 step 21: 94347599585338 + 83358599574349 step 22: 177706199159687 + 786951991607771 step 23: 964658190767458 + 854767091856469 step 24: 1819425282623927 + 7293262825249181 step 25: 9112688107873108 + 8013787018862119 step 26: 17126475126735227 + 72253762157462171 step 27: 89380237284197398 + 89379148273208398 step 28: 178759385557405796 + 697504755583957871 step 29: 876264141141363667 + 766363141141462678 step 30: 1642627282282826345 + 5436282822827262461 step 31: 7078910105110088806 + 6088800115010198707 step 32: 13167710220120287513 + 31578202102201776131 step 33: 44745912322322063644 + 44636022322321954744 step 34: 89381934644644018388 + 88381044644643918398 step 35: 177762979289287936786 + 687639782982979267771 step 36: 865402762272267204557 + 755402762272267204568 step 37: 1620805524544534409125 + 5219044354454255080261 step 38: 6839849878998789489386 13697 takes 38 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 2,495,171 times since Saturday, March 9th, 2002.)