山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1005499526

    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 1005499526:
    1005499526
    + 6259945001
    step 1: 7265444527
    + 7254445627
    step 2: 14519890154
    + 45109891541
    step 3: 59629781695
    + 59618792695
    step 4: 119248574390
    + 093475842911
    step 5: 212724417301
    + 103714427212
    step 6: 316438844513
    + 315448834613
    step 7: 631887679126
    + 621976788136
    step 8: 1253864467262
    + 2627644683521
    step 9: 3881509150783
    + 3870519051883
    step 10: 7752028202666
    + 6662028202577
    step 11: 14414056405243
    + 34250465041441
    step 12: 48664521446684
    + 48664412546684
    step 13: 97328933993368
    + 86339933982379
    step 14: 183668867975747
    + 747579768866381
    step 15: 931248636842128
    + 821248636842139
    step 16: 1752497273684267
    + 7624863727942571
    step 17: 9377361001626838
    + 8386261001637739
    step 18: 17763622003264577
    + 77546230022636771
    step 19: 95309852025901348
    + 84310952025890359
    step 20: 179620804051791707
    + 707197150408026971
    step 21: 886817954459818678
    + 876818954459718688
    step 22: 1763636908919537366
    + 6637359198096363671
    step 23: 8400996107015901037
    + 7301095107016990048
    step 24: 15702091214032891085
    + 58019823041219020751
    step 25: 73721914255251911836
    + 63811915255241912737
    step 26: 137533829510493824573
    + 375428394015928335731
    step 27: 512962223526422160304
    + 403061224625322269215
    step 28: 916023448151744429519
    + 915924447151844320619
    step 29: 1831947895303588750138
    + 8310578853035987491381
    step 30: 10142526748339576241519
    + 91514267593384762524101
    step 31: 101656794341724338765620
    + 026567833427143497656101
    step 32: 128224627768867836421721
    + 127124638768867726422821
    step 33: 255349266537735562844542
    + 245448265537735662943552
    step 34: 500797532075471225788094
    + 490887522174570235797005
    step 35: 991685054250041461585099
    + 990585164140052450586199
    step 36: 1982270218390093912171298
    + 8921712193900938120722891
    step 37: 10903982412291032032894189
    + 98149823023019221428930901
    step 38: 109053805435310253461825090
    + 090528164352013534508350901
    step 39: 199581969787323787970175991
    + 199571079787323787969185991
    step 40: 399153049574647575939361982
    + 289163939575746475940351993
    step 41: 688316989150394051879713975
    + 579317978150493051989613886
    step 42: 1267634967300887103869327861
    + 1687239683017880037694367621
    step 43: 2954874650318767141563695482
    + 2845963651417678130564784592
    step 44: 5800838301736445272128480074
    + 4700848212725446371038380085
    step 45: 10501686514461891643166860159
    + 95106866134619816441568610501
    step 46: 105608552649081708084735470660
    + 066074537480807180946255806501
    step 47: 171683090129888889030991277161
    + 161772199030988888921090386171
    step 48: 333455289160877777952081663332
    + 233366180259777778061982554333
    step 49: 566821469420655556014064217665
    + 566712460410655556024964128665
    step 50: 1133533929831311112039028346330
    + 0336438209302111131389293353311
    step 51: 1469972139133422243428321699641
    + 1469961238243422243319312799641
    step 52: 2939933377376844486747634499282
    + 2829944367476844486737733399392
    step 53: 5769877744853688973485367898674
    + 4768987635843798863584477789675
    step 54: 10538865380697487837069845688349
    + 94388654896073878479608356883501
    step 55: 104927520276771366316678202571850
    + 058175202876613663177672025729401
    step 56: 163102723153385029494350228301251
    + 152103822053494920583351327201361
    step 57: 315206545206879950077701555502612
    + 216205555107770059978602545602513
    step 58: 531412100314650010056304101105125
    + 521501101403650010056413001214135
    step 59: 1052913201718300020112717102319260
    + 0629132017172110200038171023192501
    step 60: 1682045218890410220150888125511761
    + 1671155218880510220140988125402861
    step 61: 3353200437770920440291876250914622
    + 2264190526781920440290777340023533
    step 62: 5617390964552840880582653590938155
    + 5518390953562850880482554690937165
    step 63: 11135781918115691761065208281875320
    + 02357818280256016719651181918753111
    step 64: 13493600198371708480716390200628431
    + 13482600209361708480717389100639431
    step 65: 26976200407733416961433779301267862
    + 26876210397733416961433770400267962
    step 66: 53852410805466833922867549701535824
    + 42853510794576822933866450801425835
    step 67: 96705921600043656856734000502961659
    + 95616920500043765865634000612950769
    step 68: 192322842100087422722368001115912428
    + 824219511100863227224780001248223291
    step 69: 1016542353200950649947148002364135719
    + 9175314632008417499460590023532456101
    step 70: 10191856985209368149407738025896591820
    + 02819569852083770494186390258965819101
    step 71: 13011426837293138643594128284862410921
    + 12901426848282149534683139273862411031
    step 72: 25912853685575288178277267558724821952
    + 25912842785576277287188257558635821952
    step 73: 51825696471151565465465525117360643904
    + 40934606371152556456456515117469652815
    step 74: 92760302842304121921922040234830296719
    + 91769203843204022912912140324820306729
    step 75: 184529506685508144834834180559650603448
    + 844306056955081438438441805586605925481
    step 76: 1028835563640589583273275986146256528929
    + 9298256526416895723723859850463655388201
    step 77: 10327092090057485306997135836609911917130
    + 03171911990663853179960358475009029072301
    step 78: 13499004080721338486957494311618940989431
    + 13498904981611349475968483312708040099431
    step 79: 26997909062332687962925977624326981088862
    + 26888018962342677952926978623326090979962
    step 80: 53885928024675365915852956247653072068824
    + 42886027035674265925851956357642082958835
    step 81: 96771955060349631841704912605295155027659
    + 95672055159250621940714813694306055917769
    step 82: 192444010219600253782419726299601210945428
    + 824549012106992627914287352006912010444291
    step 83: 1016993022326592881696707078306513221389719
    + 9179831223156038707076961882956232203996101
    step 84: 10196824245482631588773668961262745425385820
    + 02858352454726216986637788513628454242869101
    step 85: 13055176700208848575411457474891199668254921
    + 12945286699119847475411457584880200767155031
    step 86: 26000463399328696050822915059771400435409952
    + 25990453400417795051922805069682399336400062
    step 87: 51990916799746491102745720129453799771810014
    + 41001817799735492102754720119464799761909915
    step 88: 92992734599481983205500440248918599533719929
    + 92991733599581984204400550238918499543729929
    step 89: 185984468199063967409900990487837099077449858
    + 858944770990738784099009904769360991864489581
    step 90: 1044929239189802751508910895257198090941939439
    + 9349391490908917525980198051572089819329294401
    step 91: 10394320730098720277489108946829287910271233840
    + 04833217201978292864980198477202789003702349301
    step 92: 15227537932077013142469307424032076913973583141
    + 14138537931967023042470396424131077023973572251
    step 93: 29366075864044036184939703848163153937947155392
    + 29355174973935136184830793948163044046857066392
    step 94: 58721250837979172369770497796326197984804221784
    + 48712240848979162369779407796327197973805212785
    step 95: 107433491686958334739549905592653395958609434569
    + 965434906859593356295509945937433859686194334701
    step 96: 1072868398546551691035059851530087255644803769270
    + 0729673084465527800351589505301961556458938682701
    step 97: 1802541483012079491386649356832048812103742451971
    + 1791542473012188402386539466831949702103841452081
    step 98: 3594083956024267893773188823663998514207583904052
    + 2504093857024158993663288813773987624206593804953
    step 99: 6098177813048426887436477637437986138414177709005
    + 5009077714148316897347367746347886248403187718906
    step 100: 11107255527196743784783845383785872386817365427911
    + 11972456371868327858738354838748734769172555270111
    step 101: 23079711899065071643522200222534607155989920698022
    + 22089602998955170643522200222534617056099811797032
    step 102: 45169314898020242287044400445069224212089732495054
    + 45059423798021242296054400444078224202089841396154
    step 103: 90228738696041484583098800889147448414179573891208
    + 80219837597141484474198800889038548414069683782209
    step 104: 170448576293182969057297601778185996828249257673417
    + 714376752942828699581877106792750969281392675844071
    step 105: 884825329236011668639174708570936966109641933517488
    + 884715339146901669639075807471936866110632923528488
    step 106: 1769540668382913338278250516042873832220274857045976
    + 6795407584720222383782406150528728333192838660459671
    step 107: 8564948253103135722060656666571602165413113517505647
    + 7465057153113145612061756666560602275313013528494658
    step 108: 16030005406216281334122413333132204440726127046000305
    + 50300064072162704440223133331422143318261260450003061
    step 109: 66330069478378985774345546664554347758987387496003366
    1005499526 takes 109 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 2,061,721 times since Saturday, March 9th, 2002.)
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