山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1009150

    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 1009150:
    1009150
    + 0519001
    step 1: 1528151
    + 1518251
    step 2: 3046402
    + 2046403
    step 3: 5092805
    + 5082905
    step 4: 10175710
    + 01757101
    step 5: 11932811
    + 11823911
    step 6: 23756722
    + 22765732
    step 7: 46522454
    + 45422564
    step 8: 91945018
    + 81054919
    step 9: 172999937
    + 739999271
    step 10: 912999208
    + 802999219
    step 11: 1715998427
    + 7248995171
    step 12: 8964993598
    + 8953994698
    step 13: 17918988296
    + 69288981971
    step 14: 87207970267
    + 76207970278
    step 15: 163415940545
    + 545049514361
    step 16: 708465454906
    + 609454564807
    step 17: 1317920019713
    + 3179100297131
    step 18: 4497020316844
    + 4486130207944
    step 19: 8983150524788
    + 8874250513898
    step 20: 17857401038686
    + 68683010475871
    step 21: 86540411514557
    + 75541511404568
    step 22: 162081922919125
    + 521919229180261
    step 23: 684001152099386
    + 683990251100486
    step 24: 1367991403199872
    + 2789913041997631
    step 25: 4157904445197503
    + 3057915444097514
    step 26: 7215819889295017
    + 7105929889185127
    step 27: 14321749778480144
    + 44108487794712341
    step 28: 58430237573192485
    + 58429137573203485
    step 29: 116859375146395970
    + 079593641573958611
    step 30: 196453016720354581
    + 185453027610354691
    step 31: 381906044330709272
    + 272907033440609183
    step 32: 654813077771318455
    + 554813177770318456
    step 33: 1209626255541636911
    + 1196361455526269021
    step 34: 2405987711067905932
    + 2395097601177895042
    step 35: 4801085312245800974
    + 4790085422135801084
    step 36: 9591170734381602058
    + 8502061834370711959
    step 37: 18093232568752314017
    + 71041325786523239081
    step 38: 89134558355275553098
    + 89035557255385543198
    step 39: 178170115610661096296
    + 692690166016511071871
    step 40: 870860281627172168167
    + 761861271726182068078
    step 41: 1632721553353354236245
    + 5426324533533551272361
    step 42: 7059046086886905508606
    + 6068055096886806409507
    step 43: 13127101183773711918113
    + 31181911737738110172131
    step 44: 44309012921511822090244
    + 44209022811512921090344
    step 45: 88518035733024743180588
    + 88508134742033753081588
    step 46: 177026170475058496262176
    + 671262694850574071620771
    step 47: 848288865325632567882947
    + 749288765236523568882848
    step 48: 1597577630562156136765795
    + 5975676316512650367757951
    step 49: 7573253947074806504523746
    + 6473254056084707493523757
    step 50: 14046508003159513998047503
    + 30574089931595130080564041
    step 51: 44620597934754644078611544
    + 44511687044645743979502644
    step 52: 89132284979400388058114188
    + 88141185088300497948223198
    step 53: 177273470067700886006337386
    + 683733600688007760074372771
    step 54: 861007070755708646080710157
    + 751017080646807557070700168
    step 55: 1612024151402516203151410325
    + 5230141513026152041514202161
    step 56: 6842165664428668244665612486
    1009150 takes 56 iterations / steps to resolve into a 28 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 2,061,766 times since Saturday, March 9th, 2002.)
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