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  • REVERSAL-ADDITION PALINDROME TEST ON 13297

    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 13297:
    13297
    + 79231
    step 1: 92528
    + 82529
    step 2: 175057
    + 750571
    step 3: 925628
    + 826529
    step 4: 1752157
    + 7512571
    step 5: 9264728
    + 8274629
    step 6: 17539357
    + 75393571
    step 7: 92932928
    + 82923929
    step 8: 175856857
    + 758658571
    step 9: 934515428
    + 824515439
    step 10: 1759030867
    + 7680309571
    step 11: 9439340438
    + 8340439349
    step 12: 17779779787
    + 78797797771
    step 13: 96577577558
    + 85577577569
    step 14: 182155155127
    + 721551551281
    step 15: 903706706408
    + 804607607309
    step 16: 1708314313717
    + 7173134138071
    step 17: 8881448451788
    + 8871548441888
    step 18: 17752996893676
    + 67639869925771
    step 19: 85392866819447
    + 74491866829358
    step 20: 159884733648805
    + 508846337488951
    step 21: 668731071137756
    + 657731170137866
    step 22: 1326462241275622
    + 2265721422646231
    step 23: 3592183663921853
    + 3581293663812953
    step 24: 7173477327734806
    + 6084377237743717
    step 25: 13257854565478523
    + 32587456545875231
    step 26: 45845311111353754
    + 45735311111354854
    step 27: 91580622222708608
    + 80680722222608519
    step 28: 172261344445317127
    + 721713544443162271
    step 29: 893974888888479398
    13297 takes 29 iterations / steps to resolve into a 18 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 2,061,664 times since Saturday, March 9th, 2002.)
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