山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10000922347

    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 10000922347:
    10000922347
    + 74322900001
    step 1: 84323822348
    + 84322832348
    step 2: 168646654696
    + 696456646861
    step 3: 865103301557
    + 755103301568
    step 4: 1620206603125
    + 5213066020261
    step 5: 6833272623386
    + 6833262723386
    step 6: 13666535346772
    + 27764353566631
    step 7: 41430888913403
    + 30431988803414
    step 8: 71862877716817
    + 71861777826817
    step 9: 143724655543634
    + 436345556427341
    step 10: 580070211970975
    + 579079112070085
    step 11: 1159149324041060
    + 0601404239419511
    step 12: 1760553563460571
    + 1750643653550671
    step 13: 3511197217011242
    + 2421107127911153
    step 14: 5932304344922395
    + 5932294434032395
    step 15: 11864598778954790
    + 09745987789546811
    step 16: 21610586568501601
    + 10610586568501612
    step 17: 32221173137003213
    + 31230073137112223
    step 18: 63451246274115436
    + 63451147264215436
    step 19: 126902393538330872
    + 278033835393209621
    step 20: 404936228931540493
    + 394045139822639404
    step 21: 798981368754179897
    + 798971457863189897
    step 22: 1597952826617369794
    + 4979637166282597951
    step 23: 6577589992899967745
    + 5477699982999857756
    step 24: 12055289975899825501
    + 10552899857998255021
    step 25: 22608189833898080522
    + 22508089833898180622
    step 26: 45116279667796261144
    + 44116269776697261154
    step 27: 89232549444493522298
    + 89222539444494523298
    step 28: 178455088888988045596
    + 695540889888880554871
    step 29: 873995978777868600467
    + 764006868777879599378
    step 30: 1638002847555748199845
    + 5489918475557482008361
    step 31: 7127921323113230208206
    + 6028020323113231297217
    step 32: 13155941646226461505423
    + 32450516462264614955131
    step 33: 45606458108491076460554
    + 45506467019480185460654
    step 34: 91112925127971261921208
    + 80212916217972152921119
    step 35: 171325841345943414842327
    + 723248414349543148523171
    step 36: 894574255695486563365498
    + 894563365684596552475498
    step 37: 1789137621380083115840996
    + 6990485113800831267319871
    step 38: 8779622735180914383160867
    + 7680613834190815372269778
    step 39: 16460236569371729755430645
    + 54603455792717396563206461
    step 40: 71063692362089126318637106
    + 60173681362198026329636017
    step 41: 131237373724287152648273123
    + 321372846251782427373732131
    step 42: 452610219976069580022005254
    + 452500220085960679912016254
    step 43: 905110440062030259934021508
    + 805120439952030260044011509
    step 44: 1710230880014060519978033017
    + 7103308799150604100880320171
    step 45: 8813539679164664620858353188
    + 8813538580264664619769353188
    step 46: 17627078259429329240627706376
    + 67360772604292392495287072671
    step 47: 84987850863721721735914779047
    + 74097741953712712736805878948
    step 48: 159085592817434434472720657995
    + 599756027274434434718295580951
    step 49: 758841620091868869191016238946
    + 649832610191968868190026148857
    step 50: 1408674230283837737381042387803
    + 3087832401837377383820324768041
    step 51: 4496506632121215121201367155844
    + 4485517631021215121212366056944
    step 52: 8982024263142430242413733212788
    + 8872123373142420342413624202898
    step 53: 17854147636284850584827357415686
    + 68651475372848505848263674145871
    step 54: 86505623009133356433091031561557
    + 75516513019033465333190032650568
    step 55: 162022136028166821766281064212125
    + 521212460182667128661820631220261
    step 56: 683234596210833950428101695432386
    + 683234596101824059338012695432386
    step 57: 1366469192312658009766114390864772
    + 2774680934116679008562132919646631
    step 58: 4141150126429337018328247310511403
    + 3041150137428238107339246210511414
    step 59: 7182300263857575125667493521022817
    + 7182201253947665215757583620032817
    step 60: 14364501517805240341425077141055634
    + 43655014177052414304250871510546341
    step 61: 58019515694857654645675948651601975
    + 57910615684957654645675849651591085
    step 62: 115930131379815309291351798303193060
    + 060391303897153192903518973131039511
    step 63: 176321435276968502194870771434232571
    + 175232434177078491205869672534123671
    step 64: 351553869454046993400740443968356242
    + 242653869344047004399640454968355153
    step 65: 594207738798093997800380898936711395
    + 593117639898083008799390897837702495
    step 66: 1187325378696177006599771796774413890
    + 0983144776971779956007716968735237811
    step 67: 2170470155667956962607488765509651701
    + 1071569055678847062696597665510740712
    step 68: 3242039211346804025304086431020392413
    + 3142930201346804035204086431129302423
    step 69: 6384969412693608060508172862149694836
    + 6384969412682718050608063962149694836
    step 70: 12769938825376326111116236824299389672
    + 27698399242863261111162367352883996721
    step 71: 40468338068239587222278604177183386393
    + 39368338177140687222278593286083386404
    step 72: 79836676245380274444557197463266772797
    + 79727766236479175544447208354267663897
    step 73: 159564442481859449989004405817534436694
    + 496634435718504400989944958184244465951
    step 74: 656198878200363850978949364001778902645
    + 546209877100463949879058363002878891656
    step 75: 1202408755300827800858007727004657794301
    + 1034977564007277008580087280035578042021
    step 76: 2237386319308104809438095007040235836322
    + 2236385320407005908349084018039136837322
    step 77: 4473771639715110717787179025079372673644
    + 4463762739705209717877170115179361773744
    step 78: 8937534379420320435664349140258734447388
    + 8837444378520419434665340230249734357398
    step 79: 17774978757940739870329689370508468804786
    + 68740886480507398692307893704975787947771
    step 80: 86515865238448138562637583075484256752557
    + 75525765248457038573626583184483256851568
    step 81: 162041630486905177136264166259967513604125
    + 521406315769952661462631771509684036140261
    step 82: 683447946256857838598895937769651549744386
    + 683447945156967739598895838758652649744386
    step 83: 1366895891413825578197791776528304199488772
    + 2778849914038256771977918755283141985986631
    step 84: 4145745805452082350175710531811446185475403
    + 3045745816441181350175710532802545085475414
    step 85: 7191491621893263700351421064613991270950817
    + 7180590721993164601241530073623981261941917
    step 86: 14372082343886428301592951138237972532892734
    + 43729823527973283115929510382468834328027341
    step 87: 58101905871859711417522461520706806860920075
    + 57002906860860702516422571411795817850910185
    step 88: 115104812732720413933945032932502624711830260
    + 062038117426205239230549339314027237218401511
    step 89: 177142930158925653164494372246529861930231771
    + 177132039168925642273494461356529851039241771
    step 90: 354274969327851295437988833603059712969473542
    + 245374969217950306338889734592158723969472453
    step 91: 599649938545801601776878568195218436938945995
    + 599549839634812591865878677106108545839946995
    step 92: 1199199778180614193642757245301326982778892990
    + 0992988772896231035427572463914160818779919911
    step 93: 2192188551076845229070329709215487801558812901
    + 1092188551087845129079230709225486701558812912
    step 94: 3284377102164690358149560418440974503117625813
    + 3185267113054790448140659418530964612017734823
    step 95: 6469644215219480806290219836971939115135360636
    + 6360635315119391796389120926080849125124469646
    step 96: 12830279530338872602679340763052788240259830282
    + 28203895204288725036704397620627883303597203821
    step 97: 41034174734627597639383738383680671543857034103
    + 30143075834517608638383738393679572643747143014
    step 98: 71177250569145206277767476777360244187604177117
    + 71177140678144206377767476777260254196505277117
    step 99: 142354391247289412655534953554620498384109454234
    + 432454901483894026455359435556214982742193453241
    step 100: 574809292731183439110894389110835481126302907475
    + 574709203621184538011983498011934381137292908475
    step 101: 1149518496352367977122877887122769862263595815950
    + 0595185953622689672217887782217797632536948159411
    step 102: 1744704449975057649340765669340567494800543975361
    + 1635793450084947650439665670439467505799444074471
    step 103: 3380497900060005299780431339780035000599988049832
    + 2389408899950005300879331340879925000600097940833
    step 104: 5769906800010010600659762680659960001200085990665
    + 5660995800021000699560862679560060100100086099675
    step 105: 11430902600031011300220625360220020101300172090340
    + 04309027100310102002206352602200311013000620903411
    step 106: 15739929700341113302426977962420331114300792993751
    10000922347 takes 106 iterations / steps to resolve into a 50 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 2,061,832 times since Saturday, March 9th, 2002.)
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