山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1009246

    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 1009246:
    1009246
    + 6429001
    step 1: 7438247
    + 7428347
    step 2: 14866594
    + 49566841
    step 3: 64433435
    + 53433446
    step 4: 117866881
    + 188668711
    step 5: 306535592
    + 295535603
    step 6: 602071195
    + 591170206
    step 7: 1193241401
    + 1041423911
    step 8: 2234665312
    + 2135664322
    step 9: 4370329634
    + 4369230734
    step 10: 8739560368
    + 8630659378
    step 11: 17370219746
    + 64791207371
    step 12: 82161427117
    + 71172416128
    step 13: 153333843245
    + 542348333351
    step 14: 695682176596
    + 695671286596
    step 15: 1391353463192
    + 2913643531931
    step 16: 4304996995123
    + 3215996994034
    step 17: 7520993989157
    + 7519893990257
    step 18: 15040887979414
    + 41497978804051
    step 19: 56538866783465
    + 56438766883565
    step 20: 112977633667030
    + 030766336779211
    step 21: 143743970446241
    + 142644079347341
    step 22: 286388049793582
    + 285397940883682
    step 23: 571785990677264
    + 462776099587175
    step 24: 1034562090264439
    + 9344620902654301
    step 25: 10379182992918740
    + 04781929928197301
    step 26: 15161112921116041
    + 14061112921116151
    step 27: 29222225842232192
    + 29123224852222292
    step 28: 58345450694454484
    + 48445449605454385
    step 29: 106790900299908869
    + 968809992009097601
    step 30: 1075600892309006470
    + 0746009032980065701
    step 31: 1821609925289072171
    + 1712709825299061281
    step 32: 3534319750588133452
    + 2543318850579134353
    step 33: 6077638601167267805
    + 5087627611068367706
    step 34: 11165266212235635511
    + 11553653221266256111
    step 35: 22718919433501891622
    + 22619810533491981722
    step 36: 45338729966993873344
    + 44337839966992783354
    step 37: 89676569933986656698
    + 89665668933996567698
    step 38: 179342238867983224396
    + 693422389768832243971
    step 39: 872764628636815468367
    + 763864518636826467278
    step 40: 1636629147273641935645
    + 5465391463727419266361
    step 41: 7102020611001061202006
    + 6002021601001160202017
    step 42: 13104042212002221404023
    + 32040412220021224040131
    step 43: 45144454432023445444154
    1009246 takes 43 iterations / steps to resolve into a 23 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 2,061,760 times since Saturday, March 9th, 2002.)
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