山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1490991

    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 1490991:
    1490991
    + 1990941
    step 1: 3481932
    + 2391843
    step 2: 5873775
    + 5773785
    step 3: 11647560
    + 06574611
    step 4: 18222171
    + 17122281
    step 5: 35344452
    + 25444353
    step 6: 60788805
    + 50888706
    step 7: 111677511
    + 115776111
    step 8: 227453622
    + 226354722
    step 9: 453808344
    + 443808354
    step 10: 897616698
    + 896616798
    step 11: 1794233496
    + 6943324971
    step 12: 8737558467
    + 7648557378
    step 13: 16386115845
    + 54851168361
    step 14: 71237284206
    + 60248273217
    step 15: 131485557423
    + 324755584131
    step 16: 456241141554
    + 455141142654
    step 17: 911382284208
    + 802482283119
    step 18: 1713864567327
    + 7237654683171
    step 19: 8951519250498
    + 8940529151598
    step 20: 17892048402096
    + 69020484029871
    step 21: 86912532431967
    + 76913423521968
    step 22: 163825955953935
    + 539359559528361
    step 23: 703185515482296
    + 692284515581307
    step 24: 1395470031063603
    + 3063601300745931
    step 25: 4459071331809534
    + 4359081331709544
    step 26: 8818152663519078
    + 8709153662518188
    step 27: 17527306326037266
    + 66273062360372571
    step 28: 83800368686409837
    + 73890468686300838
    step 29: 157690837372710675
    + 576017273738096751
    step 30: 733708111110807426
    + 624708011111807337
    step 31: 1358416122222614763
    + 3674162222216148531
    step 32: 5032578344438763294
    + 4923678344438752305
    step 33: 9956256688877515599
    + 9955157788866526599
    step 34: 19911414477744042198
    + 89124044777441411991
    step 35: 109035459255185454189
    + 981454581552954530901
    step 36: 1090490040808139985090
    + 0905899318080400940901
    step 37: 1996389358888540925991
    + 1995290458888539836991
    step 38: 3991679817777080762982
    + 2892670807777189761993
    step 39: 6884350625554270524975
    + 5794250724555260534886
    step 40: 12678601350109531059861
    + 16895013590105310687621
    step 41: 29573614940214841747482
    + 28474714841204941637592
    step 42: 58048329781419783385074
    + 47058338791418792384085
    step 43: 105106668572838575769159
    + 951967575838275866601501
    step 44: 1057074244411114442370660
    + 0660732444111144424707501
    step 45: 1717806688522258867078161
    + 1618707688522258866087171
    step 46: 3336514377044517733165332
    + 2335613377154407734156333
    step 47: 5672127754198925467321665
    + 5661237645298914577212765
    step 48: 11333365399497840044534430
    + 03443544004879499356333311
    step 49: 14776909404377339400867741
    + 14776800493377340490967741
    step 50: 29553709897754679891835482
    + 28453819897645779890735592
    step 51: 58007529795400459782571074
    + 47017528795400459792570085
    step 52: 105025058590800919575141159
    + 951141575919008095850520501
    step 53: 1056166634509809015425661660
    + 0661665245109089054366616501
    step 54: 1717831879618898069792278161
    + 1618722979608988169781387171
    step 55: 3336554859227886239573665332
    + 2335663759326887229584556333
    step 56: 5672218618554773469158221665
    + 5661228519643774558168122765
    step 57: 11333447138198548027326344430
    + 03444362372084589183174433311
    step 58: 14777809510283137210500777741
    + 14777700501273138201590877741
    step 59: 29555510011556275412091655482
    + 28455619021457265511001555592
    step 60: 58011129033013540923093211074
    + 47011239032904531033092111085
    step 61: 105022368065918071956185322159
    + 951223581659170819560863220501
    step 62: 1056245949725088891517048542660
    + 0662458407151988805279495426501
    step 63: 1718704356877077696796543969161
    + 1619693456976967707786534078171
    step 64: 3338397813854045404583078047332
    + 2337408703854045404583187938333
    step 65: 5675806517708090809166265985665
    + 5665895626619080908077156085765
    step 66: 11341702144327171717243422071430
    + 03417022434271717172344120714311
    step 67: 14758724578598888889587542785741
    1490991 takes 67 iterations / steps to resolve into a 32 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 2,061,781 times since Saturday, March 9th, 2002.)
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