山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10833

    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 10833:
    10833
    + 33801
    step 1: 44634
    + 43644
    step 2: 88278
    + 87288
    step 3: 175566
    + 665571
    step 4: 841137
    + 731148
    step 5: 1572285
    + 5822751
    step 6: 7395036
    + 6305937
    step 7: 13700973
    + 37900731
    step 8: 51601704
    + 40710615
    step 9: 92312319
    + 91321329
    step 10: 183633648
    + 846336381
    step 11: 1029970029
    + 9200799201
    step 12: 10230769230
    + 03296703201
    step 13: 13527472431
    + 13427472531
    step 14: 26954944962
    + 26944945962
    step 15: 53899890924
    + 42909899835
    step 16: 96809790759
    + 95709790869
    step 17: 192519581628
    + 826185915291
    step 18: 1018705496919
    + 9196945078101
    step 19: 10215650575020
    + 02057505651201
    step 20: 12273156226221
    + 12262265137221
    step 21: 24535421363442
    + 24436312453542
    step 22: 48971733816984
    + 48961833717984
    step 23: 97933567534968
    + 86943576533979
    step 24: 184877144068947
    + 749860441778481
    step 25: 934737585847428
    + 824748585737439
    step 26: 1759486171584867
    + 7684851716849571
    step 27: 9444337888434438
    + 8344348887334449
    step 28: 17788686775768887
    + 78886757768688771
    step 29: 96675444544457658
    + 85675444544457669
    step 30: 182350889088915327
    + 723519880988053281
    step 31: 905870770076968608
    + 806869670077078509
    step 32: 1712740440154047117
    + 7117404510440472171
    step 33: 8830144950594519288
    + 8829154950594410388
    step 34: 17659299901188929676
    + 67692988110999295671
    step 35: 85352288012188225347
    + 74352288121088225358
    step 36: 159704576133276450705
    + 507054672331675407951
    step 37: 666759248464951858656
    + 656858159464842957666
    step 38: 1323617407929794816322
    + 2236184979297047163231
    step 39: 3559802387226841979553
    + 3559791486227832089553
    step 40: 7119593873454674069106
    + 6019604764543783959117
    step 41: 13139198637998458028223
    + 32282085489973689193131
    step 42: 45421284127972147221354
    + 45312274127972148212454
    step 43: 90733558255944295433808
    + 80833459244955285533709
    step 44: 171567017500899580967517
    + 715769085998005710765171
    step 45: 887336103498905291732688
    + 886237192509894301633788
    step 46: 1773573296008799593366476
    + 6746633959978006923753771
    step 47: 8520207255986806517120247
    + 7420217156086895527020258
    step 48: 15940424412073702044140505
    + 50504144020737021442404951
    step 49: 66444568432810723486545456
    + 65454568432701823486544466
    step 50: 131899136865512546973089922
    + 229980379645215568631998131
    step 51: 361879516510728115605088053
    + 350880506511827015615978163
    step 52: 712760023022555131221066216
    + 612660122131555220320067217
    step 53: 1325420145154110351541133433
    + 3343311451530114515410245231
    step 54: 4668731596684224866951378664
    10833 takes 54 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 2,061,705 times since Saturday, March 9th, 2002.)
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