山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 800067199

    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 800067199:
    800067199
    + 991760008
    step 1: 1791827207
    + 7027281971
    step 2: 8819109178
    + 8719019188
    step 3: 17538128366
    + 66382183571
    step 4: 83920311937
    + 73911302938
    step 5: 157831614875
    + 578416138751
    step 6: 736247753626
    + 626357742637
    step 7: 1362605496263
    + 3626945062631
    step 8: 4989550558894
    + 4988550559894
    step 9: 9978101118788
    + 8878111018799
    step 10: 18856212137587
    + 78573121265881
    step 11: 97429333403468
    + 86430433392479
    step 12: 183859766795947
    + 749597667958381
    step 13: 933457434754328
    + 823457434754339
    step 14: 1756914869508667
    + 7668059684196571
    step 15: 9424974553705238
    + 8325073554794249
    step 16: 17750048108499487
    + 78499480184005771
    step 17: 96249528292505258
    + 85250529282594269
    step 18: 181500057575099527
    + 725990575750005181
    step 19: 907490633325104708
    + 807401523336094709
    step 20: 1714892156661199417
    + 7149911666512984171
    step 21: 8864803823174183588
    + 8853814713283084688
    step 22: 17718618536457268276
    + 67286275463581681771
    step 23: 85004894000038950047
    + 74005983000049840058
    step 24: 159010877000088790105
    + 501097880000778010951
    step 25: 660108757000866801056
    + 650108668000757801066
    step 26: 1310217425001624602122
    + 2212064261005247120131
    step 27: 3522281686006871722253
    + 3522271786006861822253
    step 28: 7044553472013733544506
    + 6054453373102743554407
    step 29: 13099006845116477098913
    + 31989077461154860099031
    step 30: 45088084306271337197944
    + 44979173317260348088054
    step 31: 90067257623531685285998
    + 89958258613532675276009
    step 32: 180025516237064360562007
    + 700265063460732615520081
    step 33: 880290579697796976082088
    + 880280679697796975092088
    step 34: 1760571259395593951174176
    + 6714711593955939521750671
    step 35: 8475282853351533472924847
    + 7484292743351533582825748
    step 36: 15959575596703067055750595
    + 59505755076030769557595951
    step 37: 75465330672733836613346546
    + 64564331663833727603356457
    step 38: 140029662336567564216703003
    + 300307612465765633266920041
    step 39: 440337274802333197483623044
    + 440326384791333208472733044
    step 40: 880663659593666405956356088
    + 880653659504666395956366088
    step 41: 1761317319098332801912722176
    + 6712272191082338909137131671
    step 42: 8473589510180671711049853847
    + 7483589401171760810159853748
    step 43: 15957178911352432521209707595
    + 59570790212523425311987175951
    step 44: 75527969123875857833196883546
    + 64538869133875857832196972557
    step 45: 140066838257751715665393856103
    + 301658393566517157752838660041
    step 46: 441725231824268873418232516144
    + 441615232814378862428132527144
    step 47: 883340464638647735846365043288
    + 882340563648537746836464043388
    step 48: 1765681028287185482682829086676
    + 6766809282862845817828201865671
    step 49: 8532490311150031300511030952347
    + 7432590301150031300511130942358
    step 50: 15965080612300062601022161894705
    + 50749816122010626000321608056951
    step 51: 66714896734310688601343769951656
    + 65615996734310688601343769841766
    step 52: 132330893468621377202687539793422
    + 224397935786202773126864398033231
    step 53: 356728829254824150329551937826653
    + 356628739155923051428452928827653
    step 54: 713357568410747201758004866654306
    + 603456668400857102747014865753317
    step 55: 1316814236811604304505019732407623
    + 3267042379105054034061186324186131
    step 56: 4583856615916658338566206056593754
    + 4573956506026658338566195166583854
    step 57: 9157813121943316677132401223177608
    + 8067713221042317766133491213187519
    step 58: 17225526342985634443265892436365127
    + 72156363429856234443658924362552271
    step 59: 89381889772841868886924816798917398
    + 89371989761842968886814827798818398
    step 60: 178753879534684837773739644597735796
    + 697537795446937377738486435978357871
    step 61: 876291674981622215512226080576093667
    + 766390675080622215512226189476192678
    step 62: 1642682350062244431024452270052286345
    + 5436822500722544201344422600532862461
    step 63: 7079504850784788632368874870585148806
    + 6088415850784788632368874870584059707
    step 64: 13167920701569577264737749741169208513
    + 31580296114794773746277596510702976131
    step 65: 44748216816364351011015346251872184644
    + 44648127815264351011015346361861284744
    step 66: 89396344631628702022030692613733469388
    + 88396433731629603022020782613644369398
    step 67: 177792778363258305044051475227377838786
    + 687838773722574150440503852363877297771
    step 68: 865631552085832455484555327591255136557
    + 755631552195723555484554238580255136568
    step 69: 1621263104281556010969109566171510273125
    + 5213720151716659019690106551824013621261
    step 70: 6834983255998215030659216117995523894386
    + 6834983255997116129560305128995523894386
    step 71: 13669966511995331160219521246991047788772
    + 27788774019964212591206113359911566996631
    step 72: 41458740531959543751425634606902614785403
    + 30458741620960643652415734595913504785414
    step 73: 71917482152920187403841369202816119570817
    + 71807591161820296314830478102925128471917
    step 74: 143725073314740483718671847305741248042734
    + 437240842147503748176817384047413370527341
    step 75: 580965915462244231895489231353154618570075
    + 570075816451353132984598132442264519569085
    step 76: 1151041731913597364880087363795419138139160
    + 0619318319145973637800884637953191371401511
    step 77: 1770360051059571002680972001748610509540671
    + 1760459050168471002790862001759501500630771
    step 78: 3530819101228042005471834003508112010171442
    + 2441710102118053004381745002408221019180353
    step 79: 5972529203346095009853579005916333029351795
    + 5971539203336195009753589005906433029252795
    step 80: 11944068406682290019607168011822766058604590
    + 09540685066722811086170691009228660486044911
    step 81: 21484753473405101105777859021051426544649501
    + 10594644562415012095877750110150437435748412
    step 82: 32079398035820113201655609131201863980397913
    + 31979308936810213190655610231102853089397023
    step 83: 64058706972630326392311219362304717069794936
    + 63949796071740326391211329362303627960785046
    step 84: 128008503044370652783522548724608345030579982
    + 289975030543806427845225387256073440305800821
    step 85: 417983533588177080628747935980681785336380803
    + 308083633587186089539747826080771885335389714
    step 86: 726067167175363170168495762061453670671770517
    + 715077176076354160267594861071363571761760627
    step 87: 1441144343251717330436090623132817242433531144
    + 4411353342427182313260906340337171523434411441
    step 88: 5852497685678899643696996963469988765867942585
    800067199 takes 88 iterations / steps to resolve into a 46 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 2,061,820 times since Saturday, March 9th, 2002.)
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