REVERSAL-ADDITION PALINDROME TEST ON 1003569 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 1003569: 1003569 + 9653001 step 1: 10656570 + 07565601 step 2: 18222171 + 17122281 step 3: 35344452 + 25444353 step 4: 60788805 + 50888706 step 5: 111677511 + 115776111 step 6: 227453622 + 226354722 step 7: 453808344 + 443808354 step 8: 897616698 + 896616798 step 9: 1794233496 + 6943324971 step 10: 8737558467 + 7648557378 step 11: 16386115845 + 54851168361 step 12: 71237284206 + 60248273217 step 13: 131485557423 + 324755584131 step 14: 456241141554 + 455141142654 step 15: 911382284208 + 802482283119 step 16: 1713864567327 + 7237654683171 step 17: 8951519250498 + 8940529151598 step 18: 17892048402096 + 69020484029871 step 19: 86912532431967 + 76913423521968 step 20: 163825955953935 + 539359559528361 step 21: 703185515482296 + 692284515581307 step 22: 1395470031063603 + 3063601300745931 step 23: 4459071331809534 + 4359081331709544 step 24: 8818152663519078 + 8709153662518188 step 25: 17527306326037266 + 66273062360372571 step 26: 83800368686409837 + 73890468686300838 step 27: 157690837372710675 + 576017273738096751 step 28: 733708111110807426 + 624708011111807337 step 29: 1358416122222614763 + 3674162222216148531 step 30: 5032578344438763294 + 4923678344438752305 step 31: 9956256688877515599 + 9955157788866526599 step 32: 19911414477744042198 + 89124044777441411991 step 33: 109035459255185454189 + 981454581552954530901 step 34: 1090490040808139985090 + 0905899318080400940901 step 35: 1996389358888540925991 + 1995290458888539836991 step 36: 3991679817777080762982 + 2892670807777189761993 step 37: 6884350625554270524975 + 5794250724555260534886 step 38: 12678601350109531059861 + 16895013590105310687621 step 39: 29573614940214841747482 + 28474714841204941637592 step 40: 58048329781419783385074 + 47058338791418792384085 step 41: 105106668572838575769159 + 951967575838275866601501 step 42: 1057074244411114442370660 + 0660732444111144424707501 step 43: 1717806688522258867078161 + 1618707688522258866087171 step 44: 3336514377044517733165332 + 2335613377154407734156333 step 45: 5672127754198925467321665 + 5661237645298914577212765 step 46: 11333365399497840044534430 + 03443544004879499356333311 step 47: 14776909404377339400867741 + 14776800493377340490967741 step 48: 29553709897754679891835482 + 28453819897645779890735592 step 49: 58007529795400459782571074 + 47017528795400459792570085 step 50: 105025058590800919575141159 + 951141575919008095850520501 step 51: 1056166634509809015425661660 + 0661665245109089054366616501 step 52: 1717831879618898069792278161 + 1618722979608988169781387171 step 53: 3336554859227886239573665332 + 2335663759326887229584556333 step 54: 5672218618554773469158221665 + 5661228519643774558168122765 step 55: 11333447138198548027326344430 + 03444362372084589183174433311 step 56: 14777809510283137210500777741 + 14777700501273138201590877741 step 57: 29555510011556275412091655482 + 28455619021457265511001555592 step 58: 58011129033013540923093211074 + 47011239032904531033092111085 step 59: 105022368065918071956185322159 + 951223581659170819560863220501 step 60: 1056245949725088891517048542660 + 0662458407151988805279495426501 step 61: 1718704356877077696796543969161 + 1619693456976967707786534078171 step 62: 3338397813854045404583078047332 + 2337408703854045404583187938333 step 63: 5675806517708090809166265985665 + 5665895626619080908077156085765 step 64: 11341702144327171717243422071430 + 03417022434271717172344120714311 step 65: 14758724578598888889587542785741 1003569 takes 65 iterations / steps to resolve into a 32 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 2,549,908 times since Saturday, March 9th, 2002.)