山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10000505448

    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 10000505448:
    10000505448
    + 84450500001
    step 1: 94451005449
    + 94450015449
    step 2: 188901020898
    + 898020109881
    step 3: 1086921130779
    + 9770311296801
    step 4: 10857232427580
    + 08572423275801
    step 5: 19429655703381
    + 18330755692491
    step 6: 37760411395872
    + 27859311406773
    step 7: 65619722802645
    + 54620822791656
    step 8: 120240545594301
    + 103495545042021
    step 9: 223736090636322
    + 223636090637322
    step 10: 447372181273644
    + 446372181273744
    step 11: 893744362547388
    + 883745263447398
    step 12: 1777489625994786
    + 6874995269847771
    step 13: 8652484895842557
    + 7552485984842568
    step 14: 16204970880685125
    + 52158608807940261
    step 15: 68363579688625386
    + 68352688697536386
    step 16: 136716268386161772
    + 277161683862617631
    step 17: 413877952248779403
    + 304977842259778314
    step 18: 718855794508557717
    + 717755805497558817
    step 19: 1436611600006116534
    + 4356116000061166341
    step 20: 5792727600067282875
    + 5782827600067272975
    step 21: 11575555200134555850
    + 05855543100255557511
    step 22: 17431098300390113361
    + 16331109300389013471
    step 23: 33762207600779126832
    + 23862197700670226733
    step 24: 57624405301449353565
    + 56535394410350442675
    step 25: 114159799711799796240
    + 042697997117997951411
    step 26: 156857796829797747651
    + 156747797928697758651
    step 27: 313605594758495506302
    + 203605594857495506313
    step 28: 517211189615991012615
    + 516210199516981112715
    step 29: 1033421389132972125330
    + 0335212792319831243301
    step 30: 1368634181452803368631
    + 1368633082541814368631
    step 31: 2737267263994617737262
    + 2627377164993627627372
    step 32: 5364644428988245364634
    + 4364635428898244464635
    step 33: 9729279857886489829269
    + 9629289846887589729279
    step 34: 19358569704774079558548
    + 84585597047740796585391
    step 35: 103944166752514876143939
    + 939341678415257661449301
    step 36: 1043285845167772537593240
    + 0423957352777615485823401
    step 37: 1467243197945388023416641
    + 1466143208835497913427641
    step 38: 2933386406780885936844282
    + 2824486395880876046833392
    step 39: 5757872802661761983677674
    + 4767763891671662082787575
    step 40: 10525636694333424066465249
    + 94256466042433349663652501
    step 41: 104782102736766773730117750
    + 057711037377667637201287401
    step 42: 162493140114434410931405151
    + 151504139014434411041394261
    step 43: 313997279128868821972799412
    + 214997279128868821972799313
    step 44: 528994558257737643945598725
    + 527895549346737752855499825
    step 45: 1056890107604475396801098550
    + 0558901086935744067010986501
    step 46: 1615791194540219463812085051
    + 1505802183649120454911975161
    step 47: 3121593378189339918724060212
    + 2120604278199339818733951213
    step 48: 5242197656388679737458011425
    + 5241108547379768836567912425
    step 49: 10483306203768448574025923850
    + 05832952047584486730260338401
    step 50: 16316258251352935304286262251
    + 15226268240353925315285261361
    step 51: 31542526491706860619571523612
    + 21632517591606860719462524513
    step 52: 53175044083313721339034048125
    + 52184043093312731338044057135
    step 53: 105359087176626452677078105260
    + 062501870776254626671780953501
    step 54: 167860957952881079348859058761
    + 167850958843970188259759068761
    step 55: 335711916796851267608618127522
    + 225721816806762158697619117533
    step 56: 561433733603613426306237245055
    + 550542732603624316306337334165
    step 57: 1111976466207237742612574579220
    + 0229754752162477327026646791111
    step 58: 1341731218369715069639221370331
    + 1330731229369605179638121371431
    step 59: 2672462447739320249277342741762
    + 2671472437729420239377442642762
    step 60: 5343934885468740488654785384524
    + 4254835874568840478645884393435
    step 61: 9598770760037580967300669777959
    + 9597779660037690857300670778959
    step 62: 19196550420075271824601340556918
    + 81965504310642817257002405569191
    step 63: 101162054730718089081603746126109
    + 901621647306180980817037450261101
    step 64: 1002783702036899069898641196387210
    + 0127836911468989609986302073872001
    step 65: 1130620613505888679884943270259211
    + 1129520723494889768885053160260311
    step 66: 2260141337000778448769996430519522
    + 2259150346999678448770007331410622
    step 67: 4519291684000456897540003761930144
    + 4410391673000457986540004861929154
    step 68: 8929683357000914884080008623859298
    + 8929583268000804884190007533869298
    step 69: 17859266625001719768270016157728596
    + 69582775161007286791710052666295871
    step 70: 87442041786009006559980068824024467
    + 76442042886008995560090068714024478
    step 71: 163884084672018002120070137538048945
    + 549840835731070021200810276480488361
    step 72: 713724920403088023320880414018537306
    + 603735810414088023320880304029427317
    step 73: 1317460730817176046641760718047964623
    + 3264697408170671466406717180370647131
    step 74: 4582158138987847513048477898418611754
    + 4571168148987748403157487898318512854
    step 75: 9153326287975595916205965796737124608
    + 8064217376975695026195955797826233519
    step 76: 17217543664951290942401921594563358127
    + 72185336549512910424909215946634571271
    step 77: 89402880214464201367311137541197929398
    + 89392979114573111376310246441208820498
    step 78: 178795859329037312743621383982406749896
    + 698947604289383126347213730923958597871
    step 79: 877743463618420439090835114906365347767
    + 767743563609411538090934024816364347778
    step 80: 1645487027227831977181769139722729695545
    + 5455969272279319671817791387227207845461
    step 81: 7101456299507151648999560526949937541006
    + 6001457399496250659998461517059926541017
    step 82: 13102913699003402308998022044009864082023
    + 32028046890044022089980320430099631920131
    step 83: 45130960589047424398978342474109496002154
    + 45120069490147424387989342474098506903154
    step 84: 90251030079194848786967684948208002905308
    + 80350920080284948676968784849197003015209
    step 85: 170601950159479797463936469797405005920517
    + 715029500504797964639364797974951059106071
    step 86: 885631450664277762103301267772356065026588
    + 885620560653277762103301267772466054136588
    step 87: 1771252011317555524206602535544822119163176
    + 6713619112284455352066024255557131102521771
    step 88: 8484871123602010876272626791101953221684947
    + 7494861223591011976262726780102063211784848
    step 89: 15979732347193022852535353571204016433469795
    + 59796433461040217535353525822039174323797951
    step 90: 75776165808233240387888879393243190757267746
    + 64776275709134239397888878304233280856167757
    step 91: 140552441517367479785777757697476471613435503
    + 305534316174674796757777587974763715144255041
    step 92: 446086757692042276543555345672240186757690544
    + 445096757681042276543555345672240296757680644
    step 93: 891183515373084553087110691344480483515371188
    + 881173515384084443196011780355480373515381198
    step 94: 1772357030757168996283122471699960857030752386
    + 6832570307580699961742213826998617570307532771
    step 95: 8604927338337868958025336298698578427338285157
    + 7515828337248758968926335208598687338337294068
    step 96: 16120755675586627926951671507297265765675579225
    + 52297557656756279270517615962972668557655702161
    step 97: 68418313332342907197469287470269934323331281386
    + 68318213332343996207478296479170924323331381486
    step 98: 136736526664686903404947583949440858646662662872
    + 278266266646858044949385749404309686466625637631
    step 99: 415002793311544948354333333353750545113288300503
    + 305003882311545057353333333453849445113397200514
    step 100: 720006675623090005707666666807599990226685501017
    + 710105586622099995708666666707500090326576600027
    step 101: 1430112262245190001416333333515100080553262101044
    + 4401012623550800015153333336141000915422622110341
    step 102: 5831124885795990016569666669656100995975884211385
    10000505448 takes 102 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 2,061,831 times since Saturday, March 9th, 2002.)
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