山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 9000046899

    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 9000046899:
    9000046899
    + 9986400009
    step 1: 18986446908
    + 80964468981
    step 2: 99950915889
    + 98851905999
    step 3: 198802821888
    + 888128208891
    step 4: 1086931030779
    + 9770301396801
    step 5: 10857232427580
    + 08572423275801
    step 6: 19429655703381
    + 18330755692491
    step 7: 37760411395872
    + 27859311406773
    step 8: 65619722802645
    + 54620822791656
    step 9: 120240545594301
    + 103495545042021
    step 10: 223736090636322
    + 223636090637322
    step 11: 447372181273644
    + 446372181273744
    step 12: 893744362547388
    + 883745263447398
    step 13: 1777489625994786
    + 6874995269847771
    step 14: 8652484895842557
    + 7552485984842568
    step 15: 16204970880685125
    + 52158608807940261
    step 16: 68363579688625386
    + 68352688697536386
    step 17: 136716268386161772
    + 277161683862617631
    step 18: 413877952248779403
    + 304977842259778314
    step 19: 718855794508557717
    + 717755805497558817
    step 20: 1436611600006116534
    + 4356116000061166341
    step 21: 5792727600067282875
    + 5782827600067272975
    step 22: 11575555200134555850
    + 05855543100255557511
    step 23: 17431098300390113361
    + 16331109300389013471
    step 24: 33762207600779126832
    + 23862197700670226733
    step 25: 57624405301449353565
    + 56535394410350442675
    step 26: 114159799711799796240
    + 042697997117997951411
    step 27: 156857796829797747651
    + 156747797928697758651
    step 28: 313605594758495506302
    + 203605594857495506313
    step 29: 517211189615991012615
    + 516210199516981112715
    step 30: 1033421389132972125330
    + 0335212792319831243301
    step 31: 1368634181452803368631
    + 1368633082541814368631
    step 32: 2737267263994617737262
    + 2627377164993627627372
    step 33: 5364644428988245364634
    + 4364635428898244464635
    step 34: 9729279857886489829269
    + 9629289846887589729279
    step 35: 19358569704774079558548
    + 84585597047740796585391
    step 36: 103944166752514876143939
    + 939341678415257661449301
    step 37: 1043285845167772537593240
    + 0423957352777615485823401
    step 38: 1467243197945388023416641
    + 1466143208835497913427641
    step 39: 2933386406780885936844282
    + 2824486395880876046833392
    step 40: 5757872802661761983677674
    + 4767763891671662082787575
    step 41: 10525636694333424066465249
    + 94256466042433349663652501
    step 42: 104782102736766773730117750
    + 057711037377667637201287401
    step 43: 162493140114434410931405151
    + 151504139014434411041394261
    step 44: 313997279128868821972799412
    + 214997279128868821972799313
    step 45: 528994558257737643945598725
    + 527895549346737752855499825
    step 46: 1056890107604475396801098550
    + 0558901086935744067010986501
    step 47: 1615791194540219463812085051
    + 1505802183649120454911975161
    step 48: 3121593378189339918724060212
    + 2120604278199339818733951213
    step 49: 5242197656388679737458011425
    + 5241108547379768836567912425
    step 50: 10483306203768448574025923850
    + 05832952047584486730260338401
    step 51: 16316258251352935304286262251
    + 15226268240353925315285261361
    step 52: 31542526491706860619571523612
    + 21632517591606860719462524513
    step 53: 53175044083313721339034048125
    + 52184043093312731338044057135
    step 54: 105359087176626452677078105260
    + 062501870776254626671780953501
    step 55: 167860957952881079348859058761
    + 167850958843970188259759068761
    step 56: 335711916796851267608618127522
    + 225721816806762158697619117533
    step 57: 561433733603613426306237245055
    + 550542732603624316306337334165
    step 58: 1111976466207237742612574579220
    + 0229754752162477327026646791111
    step 59: 1341731218369715069639221370331
    + 1330731229369605179638121371431
    step 60: 2672462447739320249277342741762
    + 2671472437729420239377442642762
    step 61: 5343934885468740488654785384524
    + 4254835874568840478645884393435
    step 62: 9598770760037580967300669777959
    + 9597779660037690857300670778959
    step 63: 19196550420075271824601340556918
    + 81965504310642817257002405569191
    step 64: 101162054730718089081603746126109
    + 901621647306180980817037450261101
    step 65: 1002783702036899069898641196387210
    + 0127836911468989609986302073872001
    step 66: 1130620613505888679884943270259211
    + 1129520723494889768885053160260311
    step 67: 2260141337000778448769996430519522
    + 2259150346999678448770007331410622
    step 68: 4519291684000456897540003761930144
    + 4410391673000457986540004861929154
    step 69: 8929683357000914884080008623859298
    + 8929583268000804884190007533869298
    step 70: 17859266625001719768270016157728596
    + 69582775161007286791710052666295871
    step 71: 87442041786009006559980068824024467
    + 76442042886008995560090068714024478
    step 72: 163884084672018002120070137538048945
    + 549840835731070021200810276480488361
    step 73: 713724920403088023320880414018537306
    + 603735810414088023320880304029427317
    step 74: 1317460730817176046641760718047964623
    + 3264697408170671466406717180370647131
    step 75: 4582158138987847513048477898418611754
    + 4571168148987748403157487898318512854
    step 76: 9153326287975595916205965796737124608
    + 8064217376975695026195955797826233519
    step 77: 17217543664951290942401921594563358127
    + 72185336549512910424909215946634571271
    step 78: 89402880214464201367311137541197929398
    + 89392979114573111376310246441208820498
    step 79: 178795859329037312743621383982406749896
    + 698947604289383126347213730923958597871
    step 80: 877743463618420439090835114906365347767
    + 767743563609411538090934024816364347778
    step 81: 1645487027227831977181769139722729695545
    + 5455969272279319671817791387227207845461
    step 82: 7101456299507151648999560526949937541006
    + 6001457399496250659998461517059926541017
    step 83: 13102913699003402308998022044009864082023
    + 32028046890044022089980320430099631920131
    step 84: 45130960589047424398978342474109496002154
    + 45120069490147424387989342474098506903154
    step 85: 90251030079194848786967684948208002905308
    + 80350920080284948676968784849197003015209
    step 86: 170601950159479797463936469797405005920517
    + 715029500504797964639364797974951059106071
    step 87: 885631450664277762103301267772356065026588
    + 885620560653277762103301267772466054136588
    step 88: 1771252011317555524206602535544822119163176
    + 6713619112284455352066024255557131102521771
    step 89: 8484871123602010876272626791101953221684947
    + 7494861223591011976262726780102063211784848
    step 90: 15979732347193022852535353571204016433469795
    + 59796433461040217535353525822039174323797951
    step 91: 75776165808233240387888879393243190757267746
    + 64776275709134239397888878304233280856167757
    step 92: 140552441517367479785777757697476471613435503
    + 305534316174674796757777587974763715144255041
    step 93: 446086757692042276543555345672240186757690544
    + 445096757681042276543555345672240296757680644
    step 94: 891183515373084553087110691344480483515371188
    + 881173515384084443196011780355480373515381198
    step 95: 1772357030757168996283122471699960857030752386
    + 6832570307580699961742213826998617570307532771
    step 96: 8604927338337868958025336298698578427338285157
    + 7515828337248758968926335208598687338337294068
    step 97: 16120755675586627926951671507297265765675579225
    + 52297557656756279270517615962972668557655702161
    step 98: 68418313332342907197469287470269934323331281386
    + 68318213332343996207478296479170924323331381486
    step 99: 136736526664686903404947583949440858646662662872
    + 278266266646858044949385749404309686466625637631
    step 100: 415002793311544948354333333353750545113288300503
    + 305003882311545057353333333453849445113397200514
    step 101: 720006675623090005707666666807599990226685501017
    + 710105586622099995708666666707500090326576600027
    step 102: 1430112262245190001416333333515100080553262101044
    + 4401012623550800015153333336141000915422622110341
    step 103: 5831124885795990016569666669656100995975884211385
    9000046899 takes 103 iterations / steps to resolve into a 49 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 2,061,828 times since Saturday, March 9th, 2002.)
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