山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10797

    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 10797:
    10797
    + 79701
    step 1: 90498
    + 89409
    step 2: 179907
    + 709971
    step 3: 889878
    + 878988
    step 4: 1768866
    + 6688671
    step 5: 8457537
    + 7357548
    step 6: 15815085
    + 58051851
    step 7: 73866936
    + 63966837
    step 8: 137833773
    + 377338731
    step 9: 515172504
    + 405271515
    step 10: 920444019
    + 910444029
    step 11: 1830888048
    + 8408880381
    step 12: 10239768429
    + 92486793201
    step 13: 102726561630
    + 036165627201
    step 14: 138892188831
    + 138881298831
    step 15: 277773487662
    + 266784377772
    step 16: 544557865434
    + 434568755445
    step 17: 979126620879
    + 978026621979
    step 18: 1957153242858
    + 8582423517591
    step 19: 10539576760449
    + 94406767593501
    step 20: 104946344353950
    + 059353443649401
    step 21: 164299788003351
    + 153300887992461
    step 22: 317600675995812
    + 218599576006713
    step 23: 536200252002525
    + 525200252002635
    step 24: 1061400504005160
    + 0615004050041601
    step 25: 1676404554046761
    10797 takes 25 iterations / steps to resolve into a 16 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 2,061,650 times since Saturday, March 9th, 2002.)
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