山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1003569

    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 1003569:
    1003569
    + 9653001
    step 1: 10656570
    + 07565601
    step 2: 18222171
    + 17122281
    step 3: 35344452
    + 25444353
    step 4: 60788805
    + 50888706
    step 5: 111677511
    + 115776111
    step 6: 227453622
    + 226354722
    step 7: 453808344
    + 443808354
    step 8: 897616698
    + 896616798
    step 9: 1794233496
    + 6943324971
    step 10: 8737558467
    + 7648557378
    step 11: 16386115845
    + 54851168361
    step 12: 71237284206
    + 60248273217
    step 13: 131485557423
    + 324755584131
    step 14: 456241141554
    + 455141142654
    step 15: 911382284208
    + 802482283119
    step 16: 1713864567327
    + 7237654683171
    step 17: 8951519250498
    + 8940529151598
    step 18: 17892048402096
    + 69020484029871
    step 19: 86912532431967
    + 76913423521968
    step 20: 163825955953935
    + 539359559528361
    step 21: 703185515482296
    + 692284515581307
    step 22: 1395470031063603
    + 3063601300745931
    step 23: 4459071331809534
    + 4359081331709544
    step 24: 8818152663519078
    + 8709153662518188
    step 25: 17527306326037266
    + 66273062360372571
    step 26: 83800368686409837
    + 73890468686300838
    step 27: 157690837372710675
    + 576017273738096751
    step 28: 733708111110807426
    + 624708011111807337
    step 29: 1358416122222614763
    + 3674162222216148531
    step 30: 5032578344438763294
    + 4923678344438752305
    step 31: 9956256688877515599
    + 9955157788866526599
    step 32: 19911414477744042198
    + 89124044777441411991
    step 33: 109035459255185454189
    + 981454581552954530901
    step 34: 1090490040808139985090
    + 0905899318080400940901
    step 35: 1996389358888540925991
    + 1995290458888539836991
    step 36: 3991679817777080762982
    + 2892670807777189761993
    step 37: 6884350625554270524975
    + 5794250724555260534886
    step 38: 12678601350109531059861
    + 16895013590105310687621
    step 39: 29573614940214841747482
    + 28474714841204941637592
    step 40: 58048329781419783385074
    + 47058338791418792384085
    step 41: 105106668572838575769159
    + 951967575838275866601501
    step 42: 1057074244411114442370660
    + 0660732444111144424707501
    step 43: 1717806688522258867078161
    + 1618707688522258866087171
    step 44: 3336514377044517733165332
    + 2335613377154407734156333
    step 45: 5672127754198925467321665
    + 5661237645298914577212765
    step 46: 11333365399497840044534430
    + 03443544004879499356333311
    step 47: 14776909404377339400867741
    + 14776800493377340490967741
    step 48: 29553709897754679891835482
    + 28453819897645779890735592
    step 49: 58007529795400459782571074
    + 47017528795400459792570085
    step 50: 105025058590800919575141159
    + 951141575919008095850520501
    step 51: 1056166634509809015425661660
    + 0661665245109089054366616501
    step 52: 1717831879618898069792278161
    + 1618722979608988169781387171
    step 53: 3336554859227886239573665332
    + 2335663759326887229584556333
    step 54: 5672218618554773469158221665
    + 5661228519643774558168122765
    step 55: 11333447138198548027326344430
    + 03444362372084589183174433311
    step 56: 14777809510283137210500777741
    + 14777700501273138201590877741
    step 57: 29555510011556275412091655482
    + 28455619021457265511001555592
    step 58: 58011129033013540923093211074
    + 47011239032904531033092111085
    step 59: 105022368065918071956185322159
    + 951223581659170819560863220501
    step 60: 1056245949725088891517048542660
    + 0662458407151988805279495426501
    step 61: 1718704356877077696796543969161
    + 1619693456976967707786534078171
    step 62: 3338397813854045404583078047332
    + 2337408703854045404583187938333
    step 63: 5675806517708090809166265985665
    + 5665895626619080908077156085765
    step 64: 11341702144327171717243422071430
    + 03417022434271717172344120714311
    step 65: 14758724578598888889587542785741
    1003569 takes 65 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 2,061,774 times since Saturday, March 9th, 2002.)
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