REVERSAL-ADDITION PALINDROME TEST ON 1000689 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 1000689: 1000689 + 9860001 step 1: 10860690 + 09606801 step 2: 20467491 + 19476402 step 3: 39943893 + 39834993 step 4: 79778886 + 68887797 step 5: 148666683 + 386666841 step 6: 535333524 + 425333535 step 7: 960667059 + 950766069 step 8: 1911433128 + 8213341191 step 9: 10124774319 + 91347742101 step 10: 101472516420 + 024615274101 step 11: 126087790521 + 125097780621 step 12: 251185571142 + 241175581152 step 13: 492361152294 + 492251163294 step 14: 984612315588 + 885513216489 step 15: 1870125532077 + 7702355210781 step 16: 9572480742858 + 8582470842759 step 17: 18154951585617 + 71658515945181 step 18: 89813467530798 + 89703576431898 step 19: 179517043962696 + 696269340715971 step 20: 875786384678667 + 766876483687578 step 21: 1642662868366245 + 5426638682662461 step 22: 7069301551028706 + 6078201551039607 step 23: 13147503102068313 + 31386020130574131 step 24: 44533523232642444 + 44424623232533544 step 25: 88958146465175988 + 88957156464185988 step 26: 177915302929361976 + 679163929203519771 step 27: 857079232132881747 + 747188231232970758 step 28: 1604267463365852505 + 5052585633647624061 step 29: 6656853097013476566 + 6656743107903586566 step 30: 13313596204917063132 + 23136071940269531331 step 31: 36449668145186594463 + 36449568154186694463 step 32: 72899236299373288926 + 62988237399263299827 step 33: 135887473698636588753 + 357885636896374788531 step 34: 493773110595011377284 + 482773110595011377394 step 35: 976546221190022754678 + 876457220091122645679 step 36: 1853003441281145400357 + 7530045411821443003581 step 37: 9383048853102588403938 + 8393048852013588403839 step 38: 17776097705116176807777 + 77770867161150779067771 step 39: 95546964866266955875548 + 84557855966266846964559 step 40: 180104820832533802840107 + 701048208335238028401081 step 41: 881153029167771831241188 + 881142138177761920351188 step 42: 1762295167345533751592376 + 6732951573355437615922671 step 43: 8495246740700971367515047 + 7405157631790070476425948 step 44: 15900404372491041843940995 + 59904934814019427340400951 step 45: 75805339186510469184341946 + 64914348196401568193350857 step 46: 140719687382912037377692803 + 308296773730219283786917041 step 47: 449016461113131321164609844 + 448906461123131311164610944 step 48: 897922922236262632329220788 + 887022923236262632229229798 step 49: 1784945845472525264558450586 + 6850548554625252745485494871 step 50: 8635494400097778010043945457 + 7545493400108777900044945368 step 51: 16180987800206555910088890825 + 52809888001955560200878908161 step 52: 68990875802162116110967798986 + 68989776901161126120857809986 step 53: 137980652703323242231825608972 + 279806528132242323307256089731 step 54: 417787180835565565539081698703 + 307896180935565565538081787714 step 55: 725683361771131131077163486417 + 714684361770131131177163386527 step 56: 1440367723541262262254326872944 + 4492786234522622621453277630441 step 57: 5933153958063884883707604503385 + 5833054067073884883608593513395 step 58: 11766208025137769767316198016780 + 08761089161376796773152080266711 step 59: 20527297186514566540468278283491 + 19438287286404566541568179272502 step 60: 39965584472919133082036457555993 + 39955575463028033191927448556993 step 61: 79921159935947166273963906112986 + 68921160936937266174953995112997 step 62: 148842320872884432448917901225983 + 389522109719844234488278023248841 step 63: 538364430592728666937195924474824 + 428474429591739666827295034463835 step 64: 966838860184468333764490958938659 + 956839859094467333864481068838669 step 65: 1923678719278935667628972027777328 + 8237777202798267665398729178763291 step 66: 10161455922077203333027701206540619 + 91604560210772033330277022955416101 step 67: 101766016132849236663304724161956720 + 027659161427403366632948231610667101 step 68: 129425177560252603296252955772623821 + 128326277559252692306252065771524921 step 69: 257751455119505295602505021544148742 + 247841445120505206592505911554157752 step 70: 505592900240010502195010933098306494 + 494603890339010591205010042009295505 step 71: 1000196790579021093400020975107601999 + 9991067015790200043901209750976910001 step 72: 10991263806369221137301230726084512000 + 00021548062703210373112296360836219901 step 73: 11012811869072431510413527086920731901 + 10913702968072531401513427096811821011 step 74: 21926514837144962911926954183732552912 + 21925523738145962911926944173841562912 step 75: 43852038575290925823853898357574115824 + 42851147575389835832852909257583025834 step 76: 86703186150680761656706807615157141658 + 85614175151670860765616708605168130768 step 77: 172317361302351622422323516220325272426 + 624272523022615323224226153203163713271 step 78: 796589884324966945646549669423488985697 1000689 takes 78 iterations / steps to resolve into a 39 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 2,543,529 times since Saturday, March 9th, 2002.)