山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1297

    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 1297:
    1297
    + 7921
    step 1: 9218
    + 8129
    step 2: 17347
    + 74371
    step 3: 91718
    + 81719
    step 4: 173437
    + 734371
    step 5: 907808
    + 808709
    step 6: 1716517
    + 7156171
    step 7: 8872688
    + 8862788
    step 8: 17735476
    + 67453771
    step 9: 85189247
    + 74298158
    step 10: 159487405
    + 504784951
    step 11: 664272356
    + 653272466
    step 12: 1317544822
    + 2284457131
    step 13: 3602001953
    + 3591002063
    step 14: 7193004016
    + 6104003917
    step 15: 13297007933
    + 33970079231
    step 16: 47267087164
    + 46178076274
    step 17: 93445163438
    + 83436154439
    step 18: 176881317877
    + 778713188671
    step 19: 955594506548
    + 845605495559
    step 20: 1801200002107
    + 7012000021081
    step 21: 8813200023188
    1297 takes 21 iterations / steps to resolve into a 13 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 2,061,647 times since Saturday, March 9th, 2002.)
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