REVERSAL-ADDITION PALINDROME TEST ON 1001699 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 1001699: 1001699 + 9961001 step 1: 10962700 + 00726901 step 2: 11689601 + 10698611 step 3: 22388212 + 21288322 step 4: 43676534 + 43567634 step 5: 87244168 + 86144278 step 6: 173388446 + 644883371 step 7: 818271817 + 718172818 step 8: 1536444635 + 5364446351 step 9: 6900890986 + 6890980096 step 10: 13791871082 + 28017819731 step 11: 41809690813 + 31809690814 step 12: 73619381627 + 72618391637 step 13: 146237773264 + 462377732641 step 14: 608615505905 + 509505516806 step 15: 1118121022711 + 1172201218111 step 16: 2290322240822 + 2280422230922 step 17: 4570744471744 + 4471744470754 step 18: 9042488942498 + 8942498842409 step 19: 17984987784907 + 70948778948971 step 20: 88933766733878 + 87833766733988 step 21: 176767533467866 + 668764335767671 step 22: 845531869235537 + 735532968135548 step 23: 1581064837371085 + 5801737384601851 step 24: 7382802221972936 + 6392791222082837 step 25: 13775593444055773 + 37755044439557731 step 26: 51530637883613504 + 40531638873603515 step 27: 92062276757217019 + 91071275767226029 step 28: 183133552524443048 + 840344425255331381 step 29: 1023477977779774429 + 9244779777797743201 step 30: 10268257755577517630 + 03671577555775286201 step 31: 13939835311352803831 + 13830825311353893931 step 32: 27770660622706697762 + 26779660722606607772 step 33: 54550321345313305534 + 43550331354312305545 step 34: 98100652699625611079 + 97011652699625600189 step 35: 195112305399251211268 + 862112152993503211591 step 36: 1057224458392754422859 + 9582244572938544227501 step 37: 10639469031331298650360 + 06305689213313096493601 step 38: 16945158244644395143961 + 16934159344644285154961 step 39: 33879317589288680298922 + 22989208688298571397833 step 40: 56868526277587251696755 + 55769615278577262586865 step 41: 112638141556164514283620 + 026382415461655141836211 step 42: 139020557017819656119831 + 138911656918710755020931 step 43: 277932213936530411140762 + 267041114035639312239772 step 44: 544973327972169723380534 + 435083327961279723379445 step 45: 980056655933449446759979 + 979957644944339556650089 step 46: 1960014300877789003410068 + 8600143009877780034100691 step 47: 10560157310755569037510759 + 95701573096555701375106501 step 48: 106261730407311270412617260 + 062716214072113704037162601 step 49: 168977944479424974449779861 1001699 takes 49 iterations / steps to resolve into a 27 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 2,550,012 times since Saturday, March 9th, 2002.)