REVERSAL-ADDITION PALINDROME TEST ON 18060009890 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 18060009890: 18060009890 + 09890006081 step 1: 27950015971 + 17951005972 step 2: 45901021943 + 34912010954 step 3: 80813032897 + 79823031808 step 4: 160636064705 + 507460636061 step 5: 668096700766 + 667007690866 step 6: 1335104391632 + 2361934015331 step 7: 3697038406963 + 3696048307963 step 8: 7393086714926 + 6294176803937 step 9: 13687263518863 + 36881536278631 step 10: 50568799797494 + 49479799786505 step 11: 100048599583999 + 999385995840001 step 12: 1099434595424000 + 0004245954349901 step 13: 1103680549773901 + 1093779450863011 step 14: 2197460000636912 + 2196360000647912 step 15: 4393820001284824 + 4284821000283934 step 16: 8678641001568758 + 8578651001468768 step 17: 17257292003037526 + 62573030029275271 step 18: 79830322032312797 + 79721323022303897 step 19: 159551645054616694 + 496616450546155951 step 20: 656168095600772645 + 546277006590861656 step 21: 1202445102191634301 + 1034361912015442021 step 22: 2236807014207076322 + 2236707024107086322 step 23: 4473514038314162644 + 4462614138304153744 step 24: 8936128176618316388 + 8836138166718216398 step 25: 17772266343336532786 + 68723563334366227771 step 26: 86495829677702760557 + 75506720777692859468 step 27: 162002550455395620025 + 520026593554055200261 step 28: 682029144009450820286 + 682028054900441920286 step 29: 1364057198909892740572 + 2750472989098917504631 step 30: 4114530188008810245203 + 3025420188008810354114 step 31: 7139950376017620599317 + 7139950267106730599317 step 32: 14279900643124351198634 + 43689115342134600997241 step 33: 57969015985258952195875 + 57859125985258951096975 step 34: 115828141970517903292850 + 058292309715079141828511 step 35: 174120451685597045121361 + 163121540795586154021471 step 36: 337241992481183199142832 + 238241991381184299142733 step 37: 575483983862367498285565 + 565582894763268389384575 step 38: 1141066878625635887670140 + 0410767885365268786601411 step 39: 1551834763990904674271551 + 1551724764090993674381551 step 40: 3103559528081898348653102 + 2013568438981808259553013 step 41: 5117127967063706608206115 + 5116028066073607697217115 step 42: 10233156033137314305423230 + 03232450341373133065133201 step 43: 13465606374510447370556431 + 13465507374401547360656431 step 44: 26931113748911994731212862 + 26821213749911984731113962 step 45: 53752327498823979462326824 + 42862326497932889472325735 step 46: 96614653996756868934652559 + 95525643986865769935641669 step 47: 192140297983622638870294228 + 822492078836226389792041291 step 48: 1014632376819849028662335519 + 9155332668209489186732364101 step 49: 10169965045029338215394699620 + 02699649351283392054056996101 step 50: 12869614396312730269451695721 + 12759615496203721369341696821 step 51: 25629229892516451638793392542 + 24529339783615461529892292652 step 52: 50158569676131913168685685194 + 49158658686131913167696585105 step 53: 99317228362263826336382270299 + 99207228363362836226382271399 step 54: 198524456725626662562764541698 + 896145467265266626527654425891 step 55: 1094669923990893289090418967589 + 9857698140909823980993299664901 step 56: 10952368064900717270083718632490 + 09423681738007271700946086325901 step 57: 20376049802907988971029804958391 + 19385940892017988970920894067302 step 58: 39761990694925977941950699025693 + 39652099605914977952949609916793 step 59: 79414090300840955894900308942486 + 68424980300949855904800309041497 step 60: 147839070601790811799700617983983 + 389389716007997118097106070938741 step 61: 537228786609787929896806688922724 + 427229886608698929787906687822735 step 62: 964458673218486859684713376745459 + 954547673317486958684812376854469 step 63: 1919006346535973818369525753599928 + 8299953575259638183795356436009191 step 64: 10218959921795612002164882189609119 + 91190698128846120021659712995981201 step 65: 101409658050641732023824595185590320 + 023095581595428320237146050856904101 step 66: 124505239646070052260970646042494421 + 124494240646079062250070646932505421 step 67: 248999480292149114511041292974999842 + 248999479292140115411941292084999842 step 68: 497998959584289229922982585059999684 + 486999950585289229922982485959899794 step 69: 984998910169578459845965071019899478 + 874998910170569548954875961019899489 step 70: 1859997820340148008800841032039798967 + 7698979302301480088008410430287999581 step 71: 9558977122641628096809251462327798548 + 8458977232641529086908261462217798559 step 72: 18017954355283157183717512924545597107 + 70179554542921571738175138255345971081 step 73: 88197508898204728921892651179891568188 + 88186519897115629812982740289880579188 step 74: 176384028795320358734875391469772147376 + 673741277964193578437853023597820483671 step 75: 850125306759513937172728415067592631047 + 740136295760514827271739315957603521058 step 76: 1590261602520028764444467731025196152105 + 5012516915201377644444678200252061620951 step 77: 6602778517721406408889145931277257773056 + 6503777527721395419888046041277158772066 step 78: 13106556045442801828777191972554416545122 + 22154561445527919177782810824454065560131 step 79: 35261117490970721006560002797008482105253 + 35250128480079720006560012707909471116253 step 80: 70511245971050441013120015504917953221506 + 60512235971940551002131014405017954211507 step 81: 131023481942990992015251029909935907433013 + 310334709539909920152510299099249184320131 step 82: 441358191482900912167761329009185091753144 + 441357190581900923167761219009284191853144 step 83: 882715382064801835335522548018469283606288 + 882606382964810845225533538108460283517288 step 84: 1765321765029612680561056086126929567123576 + 6753217659296216806501650862169205671235671 step 85: 8518539424325829487062706948296135238359247 + 7429538325316928496072607849285234249358158 step 86: 15948077749642757983135314797581369487717405 + 50471778496318579741353138975724694777084951 step 87: 66419856245961337724488453773306064264802356 + 65320846246060337735488442773316954265891466 step 88: 131740702492021675459976896546623018530693822 + 228396035810326645698679954576120294207047131 step 89: 360136738302348321158656851122743312737740953 + 359047737213347221158656851123843203837631063 step 90: 719184475515695542317313702246586516575372016 + 610273575615685642207313713245596515574481917 step 91: 1329458051131381184524627415492183032149853933 + 3393589412303812945147264254811831311508549231 step 92: 4723047463435194129671891670304014343658403164 + 4613048563434104030761981769214915343647403274 step 93: 9336096026869298160433873439518929687305806438 + 8346085037869298159343783340618929686206906339 step 94: 17682181064738596319777656780137859373512712777 + 77721721537395873108765677791369583746018128671 step 95: 95403902602134469428543334571507443119530841448 + 84414803591134470517543334582496443120620930459 step 96: 179818706193268939946086669154003886240151771907 + 709177151042688300451966680649939862391607818971 step 97: 888995857235957240398053349803943748631759590878 + 878095957136847349308943350893042759532758599888 step 98: 1767091814372804589706996700696986508164518190766 + 6670918154618056896960076996079854082734181907671 step 99: 8438009968990861486667073696776840590898700098437 + 7348900078980950486776963707666841680998699008348 step 100: 15786910047971811973444037404443682271897399106785 + 58760199379817228634440473044437911817974001968751 step 101: 74547109427789040607884510448881594089871401075536 + 63557010417898049518884401548870604098772490174547 step 102: 138104119845687090126768911997752198188643891250083 + 380052198346881891257799119867621090786548911401831 step 103: 518156318192568981384568031865373288975192802651914 + 419156208291579882373568130865483189865291813651815 step 104: 937312526484148863758136162730856478840484616303729 + 927303616484048874658037261631857368841484625213739 step 105: 1864616142968197738416173424362713847681969241517468 + 8647151429691867483172634243716148377918692416164681 step 106: 10511767572660065221588807668078862225600661657682149 + 94128675616600652226887086670888512256006627576711501 step 107: 104640443189260717448475894338967374481607289234393650 + 056393432982706184473769833498574844717062981344046401 step 108: 161033876171966901922245727837542219198670270578440051 + 150044875072076891912245738727542229109669171678330161 step 109: 311078751244043793834491466565084448308339442256770212 + 212077652244933803844480565664194438397340442157870113 step 110: 523156403488977597678972032229278886705679884414640325 + 523046414488976507688872922230279876795779884304651325 step 111: 1046202817977954105367844954459558763501459768719291650 + 0561929178679541053678559544594487635014597797182026401 step 112: 1608131996657495159046404499054046398516057565901318051 + 1508131095657506158936404509944046409515947566991318061 step 113: 3116263092315001317982809008998092808032005132892636112 + 2116362982315002308082908998009082897131005132903626113 step 114: 5232626074630003626065718007007175705163010265796262225 + 5222626975620103615075717007008175606263000364706262325 step 115: 10455253050250107241141435014015351311426010630502524550 + 05542520503601062411315351041053414114270105205035255401 step 116: 15997773553851169652456786055068765425696115835537779951 18060009890 takes 116 iterations / steps to resolve into a 56 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 2,542,546 times since Saturday, March 9th, 2002.)