山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 6999

    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 6999:
    6999
    + 9996
    step 1: 16995
    + 59961
    step 2: 76956
    + 65967
    step 3: 142923
    + 329241
    step 4: 472164
    + 461274
    step 5: 933438
    + 834339
    step 6: 1767777
    + 7777671
    step 7: 9545448
    + 8445459
    step 8: 17990907
    + 70909971
    step 9: 88900878
    + 87800988
    step 10: 176701866
    + 668107671
    step 11: 844809537
    + 735908448
    step 12: 1580717985
    + 5897170851
    step 13: 7477888836
    + 6388887747
    step 14: 13866776583
    + 38567766831
    step 15: 52434543414
    + 41434543425
    step 16: 93869086839
    + 93868096839
    step 17: 187737183678
    + 876381737781
    step 18: 1064118921459
    + 9541298114601
    step 19: 10605417036060
    + 06063071450601
    step 20: 16668488486661
    6999 takes 20 iterations / steps to resolve into a 14 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 2,061,643 times since Saturday, March 9th, 2002.)
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