REVERSAL-ADDITION PALINDROME TEST ON 1036974 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 1036974: 1036974 + 4796301 step 1: 5833275 + 5723385 step 2: 11556660 + 06665511 step 3: 18222171 + 17122281 step 4: 35344452 + 25444353 step 5: 60788805 + 50888706 step 6: 111677511 + 115776111 step 7: 227453622 + 226354722 step 8: 453808344 + 443808354 step 9: 897616698 + 896616798 step 10: 1794233496 + 6943324971 step 11: 8737558467 + 7648557378 step 12: 16386115845 + 54851168361 step 13: 71237284206 + 60248273217 step 14: 131485557423 + 324755584131 step 15: 456241141554 + 455141142654 step 16: 911382284208 + 802482283119 step 17: 1713864567327 + 7237654683171 step 18: 8951519250498 + 8940529151598 step 19: 17892048402096 + 69020484029871 step 20: 86912532431967 + 76913423521968 step 21: 163825955953935 + 539359559528361 step 22: 703185515482296 + 692284515581307 step 23: 1395470031063603 + 3063601300745931 step 24: 4459071331809534 + 4359081331709544 step 25: 8818152663519078 + 8709153662518188 step 26: 17527306326037266 + 66273062360372571 step 27: 83800368686409837 + 73890468686300838 step 28: 157690837372710675 + 576017273738096751 step 29: 733708111110807426 + 624708011111807337 step 30: 1358416122222614763 + 3674162222216148531 step 31: 5032578344438763294 + 4923678344438752305 step 32: 9956256688877515599 + 9955157788866526599 step 33: 19911414477744042198 + 89124044777441411991 step 34: 109035459255185454189 + 981454581552954530901 step 35: 1090490040808139985090 + 0905899318080400940901 step 36: 1996389358888540925991 + 1995290458888539836991 step 37: 3991679817777080762982 + 2892670807777189761993 step 38: 6884350625554270524975 + 5794250724555260534886 step 39: 12678601350109531059861 + 16895013590105310687621 step 40: 29573614940214841747482 + 28474714841204941637592 step 41: 58048329781419783385074 + 47058338791418792384085 step 42: 105106668572838575769159 + 951967575838275866601501 step 43: 1057074244411114442370660 + 0660732444111144424707501 step 44: 1717806688522258867078161 + 1618707688522258866087171 step 45: 3336514377044517733165332 + 2335613377154407734156333 step 46: 5672127754198925467321665 + 5661237645298914577212765 step 47: 11333365399497840044534430 + 03443544004879499356333311 step 48: 14776909404377339400867741 + 14776800493377340490967741 step 49: 29553709897754679891835482 + 28453819897645779890735592 step 50: 58007529795400459782571074 + 47017528795400459792570085 step 51: 105025058590800919575141159 + 951141575919008095850520501 step 52: 1056166634509809015425661660 + 0661665245109089054366616501 step 53: 1717831879618898069792278161 + 1618722979608988169781387171 step 54: 3336554859227886239573665332 + 2335663759326887229584556333 step 55: 5672218618554773469158221665 + 5661228519643774558168122765 step 56: 11333447138198548027326344430 + 03444362372084589183174433311 step 57: 14777809510283137210500777741 + 14777700501273138201590877741 step 58: 29555510011556275412091655482 + 28455619021457265511001555592 step 59: 58011129033013540923093211074 + 47011239032904531033092111085 step 60: 105022368065918071956185322159 + 951223581659170819560863220501 step 61: 1056245949725088891517048542660 + 0662458407151988805279495426501 step 62: 1718704356877077696796543969161 + 1619693456976967707786534078171 step 63: 3338397813854045404583078047332 + 2337408703854045404583187938333 step 64: 5675806517708090809166265985665 + 5665895626619080908077156085765 step 65: 11341702144327171717243422071430 + 03417022434271717172344120714311 step 66: 14758724578598888889587542785741 1036974 takes 66 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 2,542,352 times since Saturday, March 9th, 2002.)