山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 15891

    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 15891:
    15891
    + 19851
    step 1: 35742
    + 24753
    step 2: 60495
    + 59406
    step 3: 119901
    + 109911
    step 4: 229812
    + 218922
    step 5: 448734
    + 437844
    step 6: 886578
    + 875688
    step 7: 1762266
    + 6622671
    step 8: 8384937
    + 7394838
    step 9: 15779775
    + 57797751
    step 10: 73577526
    + 62577537
    step 11: 136155063
    + 360551631
    step 12: 496706694
    + 496607694
    step 13: 993314388
    + 883413399
    step 14: 1876727787
    + 7877276781
    step 15: 9754004568
    + 8654004579
    step 16: 18408009147
    + 74190080481
    step 17: 92598089628
    + 82698089529
    step 18: 175296179157
    + 751971692571
    step 19: 927267871728
    + 827178762729
    step 20: 1754446634457
    + 7544366444571
    step 21: 9298813079028
    + 8209703188929
    step 22: 17508516267957
    + 75976261580571
    step 23: 93484777848528
    + 82584877748439
    step 24: 176069655596967
    + 769695556960671
    step 25: 945765212557638
    + 836755212567549
    step 26: 1782520425125187
    + 7815215240252871
    step 27: 9597735665378058
    + 8508735665377959
    step 28: 18106471330756017
    + 71065703317460181
    step 29: 89172174648216198
    + 89161284647127198
    step 30: 178333459295343396
    + 693343592954333871
    step 31: 871677052249677267
    + 762776942250776178
    step 32: 1634453994500453445
    + 5443540054993544361
    step 33: 7077994049493997806
    + 6087993949404997707
    step 34: 13165987998898995513
    + 31559989889978956131
    step 35: 44725977888877951644
    + 44615977888877952744
    step 36: 89341955777755904388
    + 88340955777755914398
    step 37: 177682911555511818786
    + 687818115555119286771
    step 38: 865501027110631105557
    + 755501136011720105568
    step 39: 1621002163122351211125
    + 5211121532213612001261
    step 40: 6832123695335963212386
    15891 takes 40 iterations / steps to resolve into a 22 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 2,061,691 times since Saturday, March 9th, 2002.)
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