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  • REVERSAL-ADDITION PALINDROME TEST ON 10971

    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 10971:
    10971
    + 17901
    step 1: 28872
    + 27882
    step 2: 56754
    + 45765
    step 3: 102519
    + 915201
    step 4: 1017720
    + 0277101
    step 5: 1294821
    + 1284921
    step 6: 2579742
    + 2479752
    step 7: 5059494
    + 4949505
    step 8: 10008999
    + 99980001
    step 9: 109989000
    + 000989901
    step 10: 110978901
    + 109879011
    step 11: 220857912
    + 219758022
    step 12: 440615934
    + 439516044
    step 13: 880131978
    + 879131088
    step 14: 1759263066
    + 6603629571
    step 15: 8362892637
    + 7362982638
    step 16: 15725875275
    + 57257852751
    step 17: 72983728026
    + 62082738927
    step 18: 135066466953
    + 359664660531
    step 19: 494731127484
    + 484721137494
    step 20: 979452264978
    + 879462254979
    step 21: 1858914519957
    + 7599154198581
    step 22: 9458068718538
    + 8358178608549
    step 23: 17816247327087
    + 78072374261871
    step 24: 95888621588958
    + 85988512688859
    step 25: 181877134277817
    + 718772431778181
    step 26: 900649566055998
    + 899550665946009
    step 27: 1800200232002007
    + 7002002320020081
    step 28: 8802202552022088
    10971 takes 28 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 2,061,661 times since Saturday, March 9th, 2002.)
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