山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10905963

    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 10905963:
    10905963
    + 36950901
    step 1: 47856864
    + 46865874
    step 2: 94722738
    + 83722749
    step 3: 178445487
    + 784544871
    step 4: 962990358
    + 853099269
    step 5: 1816089627
    + 7269806181
    step 6: 9085895808
    + 8085985809
    step 7: 17171881617
    + 71618817171
    step 8: 88790698788
    + 88789609788
    step 9: 177580308576
    + 675803085771
    step 10: 853383394347
    + 743493383358
    step 11: 1596876777705
    + 5077776786951
    step 12: 6674653564656
    + 6564653564766
    step 13: 13239307129422
    + 22492170393231
    step 14: 35731477522653
    + 35622577413753
    step 15: 71354054936406
    + 60463945045317
    step 16: 131817999981723
    + 327189999718131
    step 17: 459007999699854
    + 458996999700954
    step 18: 918004999400808
    + 808004999400819
    step 19: 1726009998801627
    + 7261088999006271
    step 20: 8987098997807898
    + 8987087998907898
    step 21: 17974186996715796
    + 69751769968147971
    step 22: 87725956964863767
    + 76736846965952778
    step 23: 164462803930816545
    + 545618039308264461
    step 24: 710080843239081006
    + 600180932348080017
    step 25: 1310261775587161023
    + 3201617855771620131
    step 26: 4511879631358781154
    + 4511878531369781154
    step 27: 9023758162728562308
    + 8032658272618573209
    step 28: 17056416435347135517
    + 71553174353461465071
    step 29: 88609590788808600588
    + 88500680888709590688
    step 30: 177110271677518191276
    + 672191815776172011771
    step 31: 849302087453690203047
    + 740302096354780203948
    step 32: 1589604183808470406995
    + 5996040748083814069851
    step 33: 7585644931892284476846
    + 6486744822981394465857
    step 34: 14072389754873678942703
    + 30724987637845798327041
    step 35: 44797377392719477269744
    + 44796277491729377379744
    step 36: 89593654884448854649488
    + 88494645884448845639598
    step 37: 178088300768897700289086
    + 680982007798867003880871
    step 38: 859070308567764704169957
    + 759961407467765803070958
    step 39: 1619031716035530507240915
    + 5190427050355306171309161
    step 40: 6809458766390836678550076
    + 6700558766380936678549086
    step 41: 13510017532771773357099162
    + 26199075337717723571001531
    step 42: 39709092870489496928100693
    + 39600182969498407829090793
    step 43: 79309275839987904757191486
    + 68419175740978993857290397
    step 44: 147728451580966898614481883
    + 388184416898669085154827741
    step 45: 535912868479635983769309624
    + 426903967389536974868219535
    step 46: 962816835869172958637529159
    + 951925736859271968538618269
    step 47: 1914742572728444927176147428
    + 8247416717294448272752474191
    step 48: 10162159290022893199928621619
    + 91612682999139822009295126101
    step 49: 101774842289162715209223747720
    + 027747322902517261982248477101
    step 50: 129522165191679977191472224821
    + 128422274191779976191561225921
    step 51: 257944439383459953383033450742
    + 247054330383359954383934449752
    step 52: 504998769766819907766967900494
    + 494009769667709918667967899405
    step 53: 999008539434529826434935799899
    + 998997539434628925434935800999
    step 54: 1998006078869158751869871600898
    + 8980061789681578519688706008991
    step 55: 10978067868550737271558577609889
    + 98890677585517273705586876087901
    step 56: 109868745454068010977145453697790
    + 097796354541779010860454547868901
    step 57: 207665099995847021837600001566691
    + 196665100006738120748599990566702
    step 58: 404330200002585142586199992133393
    + 393331299991685241585200002033404
    step 59: 797661499994270384171399994166797
    + 797661499993171483072499994166797
    step 60: 1595322999987441867243899988333594
    + 4953338899983427681447899992235951
    step 61: 6548661899970869548691799980569545
    + 5459650899971968459680799981668456
    step 62: 12008312799942838008372599962238001
    + 10083226999527380083824999721380021
    step 63: 22091539799470218092197599683618022
    + 22081638699579129081207499793519022
    step 64: 44173178499049347173405099477137044
    + 44073177499050437174394099487137144
    step 65: 88246355998099784347799198964274188
    + 88147246989199774348799089955364288
    step 66: 176393602987299558696598288919638476
    + 674836919882895696855992789206393671
    step 67: 851230522870195255552591078126032147
    + 741230621870195255552591078225032158
    step 68: 1592461144740390511105182156351064305
    + 5034601536512815011150930474411642951
    step 69: 6627062681253205522256112630762707256
    + 6527072670362116522255023521862607266
    step 70: 13154135351615322044511136152625314522
    + 22541352625163111544022351615353145131
    step 71: 35695487976778433588533487767978459653
    10905963 takes 71 iterations / steps to resolve into a 38 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.)

    DigitsNumberResult
    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 2,061,763 times since Saturday, March 9th, 2002.)
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