山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1064912

    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 1064912:
    1064912
    + 2194601
    step 1: 3259513
    + 3159523
    step 2: 6419036
    + 6309146
    step 3: 12728182
    + 28182721
    step 4: 40910903
    + 30901904
    step 5: 71812807
    + 70821817
    step 6: 142634624
    + 426436241
    step 7: 569070865
    + 568070965
    step 8: 1137141830
    + 0381417311
    step 9: 1518559141
    + 1419558151
    step 10: 2938117292
    + 2927118392
    step 11: 5865235684
    + 4865325685
    step 12: 10730561369
    + 96316503701
    step 13: 107047065070
    + 070560740701
    step 14: 177607805771
    + 177508706771
    step 15: 355116512542
    + 245215611553
    step 16: 600332124095
    + 590421233006
    step 17: 1190753357101
    + 1017533570911
    step 18: 2208286928012
    + 2108296828022
    step 19: 4316583756034
    + 4306573856134
    step 20: 8623157612168
    + 8612167513268
    step 21: 17235325125436
    + 63452152353271
    step 22: 80687477478707
    + 70787477478608
    step 23: 151474954957315
    + 513759459474151
    step 24: 665234414431466
    + 664134414432566
    step 25: 1329368828864032
    + 2304688288639231
    step 26: 3634057117503263
    + 3623057117504363
    step 27: 7257114235007626
    + 6267005324117527
    step 28: 13524119559125153
    + 35152195591142531
    step 29: 48676315150267684
    + 48676205151367684
    step 30: 97352520301635368
    + 86353610302525379
    step 31: 183706130604160747
    + 747061406031607381
    step 32: 930767536635768128
    + 821867536635767039
    step 33: 1752635073271535167
    + 7615351723705362571
    step 34: 9367986796976897738
    + 8377986796976897639
    step 35: 17745973593953795377
    + 77359735939537954771
    step 36: 95105709533491750148
    + 84105719433590750159
    step 37: 179211428967082500307
    + 703005280769824112971
    step 38: 882216709736906613278
    + 872316609637907612288
    step 39: 1754533319374814225566
    + 6655224184739133354571
    step 40: 8409757504113947580137
    + 7310857493114057579048
    step 41: 15720614997228005159185
    + 58195150082279941602751
    step 42: 73915765079507946761936
    + 63916764970597056751937
    step 43: 137832530050105003513873
    + 378315300501050035238731
    step 44: 516147830551155038752604
    + 406257830551155038741615
    step 45: 922405661102310077494219
    + 912494770013201166504229
    step 46: 1834900431115511243998448
    + 8448993421155111340094381
    step 47: 10283893852270622584092829
    + 92829048522607225839838201
    step 48: 103112942374877848423931030
    + 030139324848778473249211301
    step 49: 133252267223656321673142331
    + 133241376123656322762252331
    step 50: 266493643347312644435394662
    + 266493534446213743346394662
    step 51: 532987177793526387781789324
    + 423987187783625397771789235
    step 52: 956974365577151785553578559
    + 955875355587151775563479659
    step 53: 1912849721164303561117058218
    + 8128507111653034611279482191
    step 54: 10041356832817338172396540409
    + 90404569327183371823865314001
    step 55: 100445926160000709996261854410
    + 014458162699907000061629544001
    step 56: 114904088859907710057891398411
    + 114893198750017709958880409411
    step 57: 229797287609925420016771807822
    + 228708177610024529906782797922
    step 58: 458505465219949949923554605744
    + 447506455329949949912564505854
    step 59: 906011920549899899836119111598
    + 895111911638998998945029110609
    step 60: 1801123832188898898781148222207
    + 7022228411878988988812383211081
    step 61: 8823352244067887887593531433288
    + 8823341353957887887604422533288
    step 62: 17646693598025775775197953966576
    + 67566935979157757752089539664671
    step 63: 85213629577183533527287493631247
    + 74213639478272533538177592631258
    step 64: 159427269055456067065465086262505
    + 505262680564560760654550962724951
    step 65: 664689949620016827720016048987456
    + 654789840610027728610026949986466
    step 66: 1319479790230044556330042998973922
    + 2293798992400336554400320979749131
    step 67: 3613278782630381110730363978723053
    + 3503278793630370111830362878723163
    step 68: 7116557576260751222560726857446216
    + 6126447586270652221570626757556117
    step 69: 13243005162531403444131353615002333
    + 33320051635313144430413526150034231
    step 70: 46563056797844547874544879765036564
    1064912 takes 70 iterations / steps to resolve into a 35 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 2,061,792 times since Saturday, March 9th, 2002.)
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