山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 13293

    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 13293:
    13293
    + 39231
    step 1: 52524
    + 42525
    step 2: 95049
    + 94059
    step 3: 189108
    + 801981
    step 4: 991089
    + 980199
    step 5: 1971288
    + 8821791
    step 6: 10793079
    + 97039701
    step 7: 107832780
    + 087238701
    step 8: 195071481
    + 184170591
    step 9: 379242072
    + 270242973
    step 10: 649485045
    + 540584946
    step 11: 1190069991
    + 1999600911
    step 12: 3189670902
    + 2090769813
    step 13: 5280440715
    + 5170440825
    step 14: 10450881540
    + 04518805401
    step 15: 14969686941
    + 14968696941
    step 16: 29938383882
    + 28838383992
    step 17: 58776767874
    + 47876767785
    step 18: 106653535659
    + 956535356601
    step 19: 1063188892260
    + 0622988813601
    step 20: 1686177705861
    + 1685077716861
    step 21: 3371255422722
    + 2272245521733
    step 22: 5643500944455
    + 5544490053465
    step 23: 11187990997920
    + 02979909978111
    step 24: 14167900976031
    + 13067900976141
    step 25: 27235801952172
    + 27125910853272
    step 26: 54361712805444
    + 44450821716345
    step 27: 98812534521789
    + 98712543521889
    step 28: 197525078043678
    + 876340870525791
    step 29: 1073865948569469
    + 9649658495683701
    step 30: 10723524444253170
    + 07135244442532701
    step 31: 17858768886785871
    13293 takes 31 iterations / steps to resolve into a 17 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 2,061,671 times since Saturday, March 9th, 2002.)
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