REVERSAL-ADDITION PALINDROME TEST ON 1008628 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 1008628: 1008628 + 8268001 step 1: 9276629 + 9266729 step 2: 18543358 + 85334581 step 3: 103877939 + 939778301 step 4: 1043656240 + 0426563401 step 5: 1470219641 + 1469120741 step 6: 2939340382 + 2830439392 step 7: 5769779774 + 4779779675 step 8: 10549559449 + 94495594501 step 9: 105045153950 + 059351540501 step 10: 164396694451 + 154496693461 step 11: 318893387912 + 219783398813 step 12: 538676786725 + 527687676835 step 13: 1066364463560 + 0653644636601 step 14: 1720009100161 + 1610019000271 step 15: 3330028100432 + 2340018200333 step 16: 5670046300765 + 5670036400765 step 17: 11340082701530 + 03510728004311 step 18: 14850810705841 + 14850701805841 step 19: 29701512511682 + 28611521510792 step 20: 58313034022474 + 47422043031385 step 21: 105735077053859 + 958350770537501 step 22: 1064085847591360 + 0631957485804601 step 23: 1696043333395961 + 1695933333406961 step 24: 3391976666802922 + 2292086666791933 step 25: 5684063333594855 + 5584953333604865 step 26: 11269016667199720 + 02799176661096211 step 27: 14068193328295931 + 13959282339186041 step 28: 28027475667481972 + 27918476657472082 step 29: 55945952324954054 + 45045942325954955 step 30: 100991894650909009 + 900909056498199001 step 31: 1001900951149108010 + 0108019411590091001 step 32: 1109920362739199011 + 1109919372630299011 step 33: 2219839735369498022 + 2208949635379389122 step 34: 4428789370748887144 + 4417888470739878244 step 35: 8846677841488765388 + 8835678841487766488 step 36: 17682356682976531876 + 67813567928665328671 step 37: 85495924611641860547 + 74506814611642959458 step 38: 160002739223284820005 + 500028482322937200061 step 39: 660031221546222020066 + 660020222645122130066 step 40: 1320051444191344150132 + 2310514431914441500231 step 41: 3630565876105785650363 + 3630565875016785650363 step 42: 7261131751122571300726 + 6270031752211571311627 step 43: 13531163503334142612353 + 35321624143330536113531 step 44: 48852787646664678725884 1008628 takes 44 iterations / steps to resolve into a 23 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 2,549,963 times since Saturday, March 9th, 2002.)