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  • REVERSAL-ADDITION PALINDROME TEST ON 89

    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 89:
    89
    + 98
    step 1: 187
    + 781
    step 2: 968
    + 869
    step 3: 1837
    + 7381
    step 4: 9218
    + 8129
    step 5: 17347
    + 74371
    step 6: 91718
    + 81719
    step 7: 173437
    + 734371
    step 8: 907808
    + 808709
    step 9: 1716517
    + 7156171
    step 10: 8872688
    + 8862788
    step 11: 17735476
    + 67453771
    step 12: 85189247
    + 74298158
    step 13: 159487405
    + 504784951
    step 14: 664272356
    + 653272466
    step 15: 1317544822
    + 2284457131
    step 16: 3602001953
    + 3591002063
    step 17: 7193004016
    + 6104003917
    step 18: 13297007933
    + 33970079231
    step 19: 47267087164
    + 46178076274
    step 20: 93445163438
    + 83436154439
    step 21: 176881317877
    + 778713188671
    step 22: 955594506548
    + 845605495559
    step 23: 1801200002107
    + 7012000021081
    step 24: 8813200023188
    89 takes 24 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 2,061,587 times since Saturday, March 9th, 2002.)
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