山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10701592943

    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 10701592943:
    10701592943
    + 34929510701
    step 1: 45631103644
    + 44630113654
    step 2: 90261217298
    + 89271216209
    step 3: 179532433507
    + 705334235971
    step 4: 884866669478
    + 874966668488
    step 5: 1759833337966
    + 6697333389571
    step 6: 8457166727537
    + 7357276617548
    step 7: 15814443345085
    + 58054334441851
    step 8: 73868777786936
    + 63968777786837
    step 9: 137837555573773
    + 377375555738731
    step 10: 515213111312504
    + 405213111312515
    step 11: 920426222625019
    + 910526222624029
    step 12: 1830952445249048
    + 8409425442590381
    step 13: 10240377887839429
    + 92493878877304201
    step 14: 102734256765143630
    + 036341567652437201
    step 15: 139075824417580831
    + 138085714428570931
    step 16: 277161538846151762
    + 267151648835161772
    step 17: 544313187681313534
    + 435313186781313445
    step 18: 979626374462626979
    + 979626264473626979
    step 19: 1959252638936253958
    + 8593526398362529591
    step 20: 10552779037298783549
    + 94538789273097725501
    step 21: 105091568310396509050
    + 050905693013865190501
    step 22: 155997261324261699551
    + 155996162423162799551
    step 23: 311993423747424499102
    + 201994424747324399113
    step 24: 513987848494748898215
    + 512898847494848789315
    step 25: 1026886695989597687530
    + 0357867959895966886201
    step 26: 1384754655885564573731
    + 1373754655885564574831
    step 27: 2758509311771129148562
    + 2658419211771139058572
    step 28: 5416928523542268207134
    + 4317028622453258296145
    step 29: 9733957145995526503279
    + 9723056255995417593379
    step 30: 19457013401990944096658
    + 85669044909910431075491
    step 31: 105126058311901375172149
    + 941271573109113850621501
    step 32: 1046397631421015225793650
    + 0563975225101241367936401
    step 33: 1610372856522256593730051
    + 1500373956522256582730161
    step 34: 3110746813044513176460212
    + 2120646713154403186470113
    step 35: 5231393526198916362930325
    + 5230392636198916253931325
    step 36: 10461786162397832616861650
    + 05616861623879326168716401
    step 37: 16078647786277158785578051
    + 15087558785177268774687061
    step 38: 31166206571454427560265112
    + 21156206572445417560266113
    step 39: 52322413143899845120531225
    + 52213502154899834131422325
    step 40: 104535915298799679251953550
    + 055359152976997892519535401
    step 41: 159895068275797571771488951
    + 159884177175797572860598951
    step 42: 319779245451595144632087902
    + 209780236441595154542977913
    step 43: 529559481893190299175065815
    + 518560571992091398184955925
    step 44: 1048120053885281697360021740
    + 0471200637961825883500218401
    step 45: 1519320691847107580860240141
    + 1410420680857017481960239151
    step 46: 2929741372704125062820479292
    + 2929740282605214072731479292
    step 47: 5859481655309339135551958584
    + 4858591555319339035561849585
    step 48: 10718073210628678171113808169
    + 96180831117187682601237081701
    step 49: 106898904327816360772350889870
    + 078988053277063618723409898601
    step 50: 185886957604879979495760788471
    + 174887067594979978406759688581
    step 51: 360774025199859957902520477052
    + 250774025209759958991520477063
    step 52: 611548050409619916894040954115
    + 511459040498619916904050845116
    step 53: 1123007090908239833798091799231
    + 1329971908973389328090907003211
    step 54: 2452978999881629161888998802442
    + 2442088998881619261889998792542
    step 55: 4895067998763248423778997594984
    + 4894957998773248423678997605984
    step 56: 9790025997536496847457995200968
    + 8690025997547486946357995200979
    step 57: 18480051995083983793815990401947
    + 74910409951839738938059915008481
    step 58: 93390461946923722731875905410428
    + 82401450957813722732964916409339
    step 59: 175791912904737445464840821819767
    + 767918128048464544737409219197571
    step 60: 943710040953201990202250041017338
    + 833710140052202099102359040017349
    step 61: 1777420181005404089304609081034687
    + 7864301809064039804045001810247771
    step 62: 9641721990069443893349610891282458
    + 8542821980169433983449600991271469
    step 63: 18184543970238877876799211882553927
    + 72935528811299767877883207934548181
    step 64: 91120072781538645754682419817102108
    + 80120171891428645754683518727002119
    step 65: 171240244672967291509365938544104227
    + 722401445839563905192769276442042171
    step 66: 893641690512531196702135214986146398
    + 893641689412531207691135215096146398
    step 67: 1787283379925062404393270430082292796
    + 6972922800340723934042605299733827871
    step 68: 8760206180265786338435875729816120667
    + 7660216189275785348336875620816020678
    step 69: 16420422369541571686772751350632141345
    + 54314123605315727768617514596322402461
    step 70: 70734545974857299455390265946954543806
    + 60834545964956209355499275847954543707
    step 71: 131569091939813508810889541794909087513
    + 315780909497145988018805318939190965131
    step 72: 447350001436959496829694860734100052644
    + 446250001437068496928694959634100053744
    step 73: 893600002874027993758389820368200106388
    + 883601002863028983857399720478200006398
    step 74: 1777201005737056977615789540846400112786
    + 6872110046480459875167796507375001027771
    step 75: 8649311052217516852783586048221401140557
    + 7550411041228406853872586157122501139468
    step 76: 16199722093445923706656172205343902280025
    + 52008220934350227165660732954439022799161
    step 77: 68207943027796150872316905159782925079186
    + 68197052928795150961327805169772034970286
    step 78: 136404995956591301833644710329554960049472
    + 274940069455923017446338103195659599404631
    step 79: 411345065412514319279982813525214559454103
    + 301454955412525318289972913415214560543114
    step 80: 712800020825039637569955726940429119997217
    + 712799911924049627559965736930528020008217
    step 81: 1425599932749089265129921463870957140005434
    + 4345000417590783641299215629809472399955241
    step 82: 5770600350339872906429137093680429539960675
    + 5760699359240863907319246092789330530060775
    step 83: 11531299709580736813748383186469760070021450
    + 05412007006796468138384731863708590799213511
    step 84: 16943306716377204952133115050178350869234961
    + 16943296805387105051133125940277361760334961
    step 85: 33886603521764310003266240990455712629569922
    + 22996592621755409904266230001346712530668833
    step 86: 56883196143519719907532470991802425160238755
    + 55783206152420819907423570991791534169138865
    step 87: 112666402295940539814956041983593959329377620
    + 026773923959395389140659418935049592204666211
    step 88: 139440326255335928955615460918643551534043831
    + 138340435155346819064516559829533552623044931
    step 89: 277780761410682748020132020748177104157088762
    + 267880751401771847020231020847286014167087772
    step 90: 545661512812454595040363041595463118324176534
    + 435671423811364595140363040595454218215166545
    step 91: 981332936623819190180726082190917336539343079
    + 970343935633719091280627081091918326639233189
    step 92: 1951676872257538281461353163282835663178576268
    + 8626758713665382823613531641828357522786761591
    step 93: 10578435585922921105074884805111193185965337859
    + 95873356958139111150848847050112922958553487501
    step 94: 106451792544062032255923731855224116144518825360
    + 063528815441611422558137329552230260445297154601
    step 95: 169980607985673454814061061407454376589815979961
    + 169979518985673454704160160418454376589706089961
    step 96: 339960126971346909518221221825908753179522069922
    + 229960225971357809528122122815909643179621069933
    step 97: 569920352942704719046343344641818396359143139855
    + 558931341953693818146443343640917407249253029965
    step 98: 1128851694896398537192786688282735803608396169820
    + 0289616938063085372828866872917358936984961588211
    step 99: 1418468632959483910021653561200094740593357758031
    + 1308577533950474900021653561200193849592368648141
    step 100: 2727046166909958810043307122400288590185726406172
    + 2716046275810958820042217033400188599096616407272
    step 101: 5443092442720917630085524155800477189282342813444
    + 4443182432829817740085514255800367190272442903445
    step 102: 9886274875550735370171038411600844379554785716889
    + 9886175874559734480061148301710735370555784726889
    step 103: 19772450750110469850232186713311579750110570443778
    + 87734407501105797511331768123205896401105705427791
    step 104: 107506858251216267361563954836517476151216275871569
    + 965178572612151674715638459365163762612152858605701
    step 105: 1072685430863367942077202414201681238763369134477270
    + 0727744319633678321861024142027702497633680345862701
    step 106: 1800429750497046263938226556229383736397049480339971
    + 1799330849407936373839226556228393626407940579240081
    step 107: 3599760599904982637777453112457777362804990059580052
    + 2500859500994082637777542113547777362894099950679953
    step 108: 6100620100899065275554995226005554725699090010260005
    + 5000620100909965274555006225994555725609980010260016
    step 109: 11101240201809030550110001452000110451309070020520021
    + 12002502007090315401100025410001105503090810204210111
    step 110: 23103742208899345951210026862001215954399880224730132
    10701592943 takes 110 iterations / steps to resolve into a 53 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 2,061,834 times since Saturday, March 9th, 2002.)
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