山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 600259

    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 600259:
    600259
    + 952006
    step 1: 1552265
    + 5622551
    step 2: 7174816
    + 6184717
    step 3: 13359533
    + 33595331
    step 4: 46954864
    + 46845964
    step 5: 93800828
    + 82800839
    step 6: 176601667
    + 766106671
    step 7: 942708338
    + 833807249
    step 8: 1776515587
    + 7855156771
    step 9: 9631672358
    + 8532761369
    step 10: 18164433727
    + 72733446181
    step 11: 90897879908
    + 80997879809
    step 12: 171895759717
    + 717957598171
    step 13: 889853357888
    + 888753358988
    step 14: 1778606716876
    + 6786176068771
    step 15: 8564782785647
    + 7465872874658
    step 16: 16030655660305
    + 50306655603061
    step 17: 66337311263366
    + 66336211373366
    step 18: 132673522636732
    + 237636225376231
    step 19: 370309748012963
    + 369210847903073
    step 20: 739520595916036
    + 630619595025937
    step 21: 1370140190941973
    + 3791490910410731
    step 22: 5161631101352704
    + 4072531011361615
    step 23: 9234162112714319
    + 9134172112614329
    step 24: 18368334225328648
    + 84682352243386381
    step 25: 103050686468715029
    + 920517864686050301
    step 26: 1023568551154765330
    + 0335674511558653201
    step 27: 1359243062713418531
    + 1358143172603429531
    step 28: 2717386235316848062
    + 2608486135326837172
    step 29: 5325872370643685234
    + 4325863460732785235
    step 30: 9651735831376470469
    + 9640746731385371569
    step 31: 19292482562761842038
    + 83024816726528429291
    step 32: 102317299289290271329
    + 923172092982992713201
    step 33: 1025489392272282984530
    + 0354892822722939845201
    step 34: 1380382214995222829731
    + 1379282225994122830831
    step 35: 2759664440989345660562
    + 2650665439890444669572
    step 36: 5410329880879790330134
    + 4310330979780889230145
    step 37: 9720660860660679560279
    + 9720659760660680660279
    step 38: 19441320621321360220558
    + 85502206312312602314491
    step 39: 104943526933633962535049
    + 940535269336339625349401
    step 40: 1045478796269973587884450
    + 0544887853799626978745401
    step 41: 1590366650069600566629851
    + 1589266650069600566630951
    step 42: 3179633300139201133260802
    + 2080623311029310033369713
    step 43: 5260256611168511166630515
    + 5150366611158611166520625
    step 44: 10410623222327122333151140
    + 04115133322172322232601401
    step 45: 14525756544499444565752541
    600259 takes 45 iterations / steps to resolve into a 26 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 2,061,722 times since Saturday, March 9th, 2002.)
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