山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 151033997

    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 151033997:
    151033997
    + 799330151
    step 1: 950364148
    + 841463059
    step 2: 1791827207
    + 7027281971
    step 3: 8819109178
    + 8719019188
    step 4: 17538128366
    + 66382183571
    step 5: 83920311937
    + 73911302938
    step 6: 157831614875
    + 578416138751
    step 7: 736247753626
    + 626357742637
    step 8: 1362605496263
    + 3626945062631
    step 9: 4989550558894
    + 4988550559894
    step 10: 9978101118788
    + 8878111018799
    step 11: 18856212137587
    + 78573121265881
    step 12: 97429333403468
    + 86430433392479
    step 13: 183859766795947
    + 749597667958381
    step 14: 933457434754328
    + 823457434754339
    step 15: 1756914869508667
    + 7668059684196571
    step 16: 9424974553705238
    + 8325073554794249
    step 17: 17750048108499487
    + 78499480184005771
    step 18: 96249528292505258
    + 85250529282594269
    step 19: 181500057575099527
    + 725990575750005181
    step 20: 907490633325104708
    + 807401523336094709
    step 21: 1714892156661199417
    + 7149911666512984171
    step 22: 8864803823174183588
    + 8853814713283084688
    step 23: 17718618536457268276
    + 67286275463581681771
    step 24: 85004894000038950047
    + 74005983000049840058
    step 25: 159010877000088790105
    + 501097880000778010951
    step 26: 660108757000866801056
    + 650108668000757801066
    step 27: 1310217425001624602122
    + 2212064261005247120131
    step 28: 3522281686006871722253
    + 3522271786006861822253
    step 29: 7044553472013733544506
    + 6054453373102743554407
    step 30: 13099006845116477098913
    + 31989077461154860099031
    step 31: 45088084306271337197944
    + 44979173317260348088054
    step 32: 90067257623531685285998
    + 89958258613532675276009
    step 33: 180025516237064360562007
    + 700265063460732615520081
    step 34: 880290579697796976082088
    + 880280679697796975092088
    step 35: 1760571259395593951174176
    + 6714711593955939521750671
    step 36: 8475282853351533472924847
    + 7484292743351533582825748
    step 37: 15959575596703067055750595
    + 59505755076030769557595951
    step 38: 75465330672733836613346546
    + 64564331663833727603356457
    step 39: 140029662336567564216703003
    + 300307612465765633266920041
    step 40: 440337274802333197483623044
    + 440326384791333208472733044
    step 41: 880663659593666405956356088
    + 880653659504666395956366088
    step 42: 1761317319098332801912722176
    + 6712272191082338909137131671
    step 43: 8473589510180671711049853847
    + 7483589401171760810159853748
    step 44: 15957178911352432521209707595
    + 59570790212523425311987175951
    step 45: 75527969123875857833196883546
    + 64538869133875857832196972557
    step 46: 140066838257751715665393856103
    + 301658393566517157752838660041
    step 47: 441725231824268873418232516144
    + 441615232814378862428132527144
    step 48: 883340464638647735846365043288
    + 882340563648537746836464043388
    step 49: 1765681028287185482682829086676
    + 6766809282862845817828201865671
    step 50: 8532490311150031300511030952347
    + 7432590301150031300511130942358
    step 51: 15965080612300062601022161894705
    + 50749816122010626000321608056951
    step 52: 66714896734310688601343769951656
    + 65615996734310688601343769841766
    step 53: 132330893468621377202687539793422
    + 224397935786202773126864398033231
    step 54: 356728829254824150329551937826653
    + 356628739155923051428452928827653
    step 55: 713357568410747201758004866654306
    + 603456668400857102747014865753317
    step 56: 1316814236811604304505019732407623
    + 3267042379105054034061186324186131
    step 57: 4583856615916658338566206056593754
    + 4573956506026658338566195166583854
    step 58: 9157813121943316677132401223177608
    + 8067713221042317766133491213187519
    step 59: 17225526342985634443265892436365127
    + 72156363429856234443658924362552271
    step 60: 89381889772841868886924816798917398
    + 89371989761842968886814827798818398
    step 61: 178753879534684837773739644597735796
    + 697537795446937377738486435978357871
    step 62: 876291674981622215512226080576093667
    + 766390675080622215512226189476192678
    step 63: 1642682350062244431024452270052286345
    + 5436822500722544201344422600532862461
    step 64: 7079504850784788632368874870585148806
    + 6088415850784788632368874870584059707
    step 65: 13167920701569577264737749741169208513
    + 31580296114794773746277596510702976131
    step 66: 44748216816364351011015346251872184644
    + 44648127815264351011015346361861284744
    step 67: 89396344631628702022030692613733469388
    + 88396433731629603022020782613644369398
    step 68: 177792778363258305044051475227377838786
    + 687838773722574150440503852363877297771
    step 69: 865631552085832455484555327591255136557
    + 755631552195723555484554238580255136568
    step 70: 1621263104281556010969109566171510273125
    + 5213720151716659019690106551824013621261
    step 71: 6834983255998215030659216117995523894386
    + 6834983255997116129560305128995523894386
    step 72: 13669966511995331160219521246991047788772
    + 27788774019964212591206113359911566996631
    step 73: 41458740531959543751425634606902614785403
    + 30458741620960643652415734595913504785414
    step 74: 71917482152920187403841369202816119570817
    + 71807591161820296314830478102925128471917
    step 75: 143725073314740483718671847305741248042734
    + 437240842147503748176817384047413370527341
    step 76: 580965915462244231895489231353154618570075
    + 570075816451353132984598132442264519569085
    step 77: 1151041731913597364880087363795419138139160
    + 0619318319145973637800884637953191371401511
    step 78: 1770360051059571002680972001748610509540671
    + 1760459050168471002790862001759501500630771
    step 79: 3530819101228042005471834003508112010171442
    + 2441710102118053004381745002408221019180353
    step 80: 5972529203346095009853579005916333029351795
    + 5971539203336195009753589005906433029252795
    step 81: 11944068406682290019607168011822766058604590
    + 09540685066722811086170691009228660486044911
    step 82: 21484753473405101105777859021051426544649501
    + 10594644562415012095877750110150437435748412
    step 83: 32079398035820113201655609131201863980397913
    + 31979308936810213190655610231102853089397023
    step 84: 64058706972630326392311219362304717069794936
    + 63949796071740326391211329362303627960785046
    step 85: 128008503044370652783522548724608345030579982
    + 289975030543806427845225387256073440305800821
    step 86: 417983533588177080628747935980681785336380803
    + 308083633587186089539747826080771885335389714
    step 87: 726067167175363170168495762061453670671770517
    + 715077176076354160267594861071363571761760627
    step 88: 1441144343251717330436090623132817242433531144
    + 4411353342427182313260906340337171523434411441
    step 89: 5852497685678899643696996963469988765867942585
    151033997 takes 89 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 2,061,821 times since Saturday, March 9th, 2002.)
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