[seqfan] Re: "summer hours" NEW SEQ Z1
Ray Chandler
rayjchandler at sbcglobal.net
Fri Jun 4 15:15:38 CEST 2010
Thanks.
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Robert Gerbicz
> Sent: Friday, June 04, 2010 7:56 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: "summer hours" NEW SEQ Z1
>
> 2010/6/4 Ray Chandler <rayjchandler at sbcglobal.net>
>
> > Robert,
> > I'd love to see your code so I can understand what you mean by
> > backtracking.
> > Thanks.
> > Ray
> >
> > > -----Original Message-----
> > > From: seqfan-bounces at list.seqfan.eu
> > > [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of zak seidov
> > > Sent: Friday, June 04, 2010 7:01 AM
> > > To: seqfaneu
> > > Subject: [seqfan] Re: "summer hours" NEW SEQ Z1
> > >
> > > Robert, thanks a lot!
> > >
> > > In case A178679'll appear
> > > I suggest you submit (your great) b-file.
> > >
> > > Thanks again,
> > > Zak
> > >
> > > --- On Fri, 6/4/10, Robert Gerbicz
> <robert.gerbicz at gmail.com> wrote:
> > >
> > > > From: Robert Gerbicz <robert.gerbicz at gmail.com>
> > > > Subject: [seqfan] Re: "summer hours" NEW SEQ Z1
> > > > To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> > > > Date: Friday, June 4, 2010, 7:53 AM
> > > > 2010/6/4 zak seidov <zakseidov at yahoo.com>
> > > >
> > > > > Thanks, Jeremy et al!
> > > > >
> > > > > FYI
> > > > > Submitted, but yet not appeared:
> > > > >
> > > > > %I A178679
> > > > > %S A178679
> > > > >
> > > >
> 0,1,9,10,12,94,118,120,2217,22204,22602,26608,27004,27009,531795,
> > > > > %T A178679
> > > > >
> > > >
> 5021473,5321298,6384861,50218140,63858541,1181639052,12029699478,
> > > > > %U A178679
> > > > >
> > > > >
> > > >
> > >
> 14392731189,15114438648,283004031766,283592574694,2672433464707,2835
> > > 93
> > > > 292766
> > > > > 1
> > > > > %N A178679 Numbers n such that the binary expansion of
> > > > n starts with the
> > > > > base 3 expansion
> > > > >
> > > > of n.
> > > > > %e A178679 2217 = 100010101001 (base 2) %e A178679 2217 =
> > > > > 10001010.... (base 3) %e A178679 531795 =
> > > 10000001110101010011 (base
> > > > > 2) %e A178679 531795 = 1000000111010....... (base 3)
> %t A178679
> > > > Do[i3=IntegerDigits[n,2];l3=Length[i3];i=FromDigits[i3,3];
> > > > >
> > > >
> > >
> i2=IntegerDigits[i,2];If[i3==Take[i2,l3],Print[i]];,{n,0,10^7}];(*Ra
> > > y
> > > > > Chandler*)
> > > > > %Y A178679 Cf. A169828, A178680.
> > > > > %K A178679 nonn,new
> > > > > %O A178679 1,3
> > > > > %A A178679 Zak Seidov (zakseidov(AT)yahoo.com) and
> > > > Ray
> > > > > Chandler
> > > > > (rayjchandler(AT)sbcglobal.net), Jun 03 2010
> > > > >
> > > > > Best, Zak
> > > > >
> > > > > --- On Fri, 6/4/10, Jeremy Gardiner
> > > <jeremy.gardiner at btinternet.com>
> > > > > wrote:
> > > > >
> > > > >
> > > > > > additional terms:
> > > > > >
> > > > > > 50218140 =
> > > > > > 10111111100100010010011100 (base
> > > > 2)
> > > > > >
> > > > > > 10111111100100010
> > > > > > (base 3)
> > > > > >
> > > > > > 63858541 =
> > > > > > 11110011100110011101101101 (base
> > > > 2)
> > > > > >
> > > > > > 11110011100110011
> > > > > > (base 3)
> > > > > >
> > > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > _______________________________________________
> > > > >
> > > > > Seqfan Mailing list - http://list.seqfan.eu/
> > > > >
> > > >
> > > > By backtracking it is much easier to find the terms. It
> > > seems that the
> > > > sequence is infinite and log(a(n))/(n*log(3))->1 as n goes to
> > > > infinity.
> > > >
> > > > 1 0
> > > > 2 1
> > > > 3 9
> > > > 4 10
> > > > 5 12
> > > > 6 94
> > > > 7 118
> > > > 8 120
> > > > 9 2217
> > > > 10 22204
> > > > 11 22602
> > > > 12 26608
> > > > 13 27004
> > > > 14 27009
> > > > 15 531795
> > > > 16 5021473
> > > > 17 5321298
> > > > 18 6384861
> > > > 19 50218140
> > > > 20 63858541
> > > > 21 1181639052
> > > > 22 12029699478
> > > > 23 14392731189
> > > > 24 15114438648
> > > > 25 283004031766
> > > > 26 283592574694
> > > > 27 2672433464707
> > > > 28 2835932927661
> > > > 29 3401357393557
> > > > 30 3403118077048
> > > > 31 34031202298651
> > > > 32 34177907305884
> > > > 33 628828927111647
> > > > 34 628970727806707
> > > > 35 640942059754281
> > > > 36 6413415101294509
> > > > 37 7695204742580427
> > > > 38 8053859972911086
> > > > 39 150814873763789940
> > > > 40 150918518689173634
> > > > 41 1425003969567726048
> > > > 42 1509185516440202724
> > > > 43 1517829814013577097
> > > > 44 1818730810511453811
> > > > 45 1819666955620804033
> > > > 46 18213961158416319831
> > > > 47 341088106149793656279
> > > > 48 341773518106319625811
> > > > 49 3430482343696821859257
> > > > 50 3432531817134264871539
> > > > 51 4101354725354306413372
> > > > 52 4305366505480789205776
> > > > 53 80258672164110402588970
> > > > 54 80767897643780907174811
> > > > 55 807844505615720643096525
> > > > 56 969379900564316388001492
> > > > 57 983827164563315035761430
> > > > 58 19384246715613545348161218
> > > > 59 181880333263516583442398967
> > > > 60 193842467157061116981323140
> > > > 61 232611107180694334086303892
> > > > 62 1829231113088652066926008284
> > > > 63 2294441483028987263343198852
> > > > 64 2326230141715533657065429857
> > > > 65 42981992640685560997253517573
> > > > 66 430446715516226065846512193969
> > > > 67 438128386544979295064100336033
> > > > 68 523550358343589451306761344963
> > > > 69 10315416948273292565198720568483 70
> > > > 97344818465414394763086642378109
> > > > 71 103154172700594940776696522920238
> > > > 72 103156530844766581126329526446655
> > > > 73 123787131699149317522651630378269
> > > > 74 973448772850675493708125247767803
> > > > 75 1239622689596376846730330919987605
> > > > 76 22910049304016027325166510587926292
> > > > 77 233198808031068852294513771139964947
> > > > 78 279008562549177982759481364534210796
> > > > 79 292997573548074042531825341121972718
> > > > 80 5497243536854306497793583890982353949
> > > > 81 51803668520706074456707861449285252432
> > > > 82 51906559240207688046588431293635837165
> > > > 83 54972760042426432132244642362826030802
> > > > 84 65970699382361558594234234777867048619
> > > > 85 662616547670816873549658562755448579888
> > > > 86 662627827816878558875823766780269832020
> > > > 87 12192168049902376610289087220272297995472
> > > > 88 12432575544876426409155194485647116374452
> > > > 89 124325766703825801392085917341459368761613
> > > > 90 149190910295058310957644031668282529257430
> > > > 91 156142986761396597443131290779563629950260
> > > > 92 2925450667403347776410944394915713358358010
> > > > 93 27624655350353299498366621325338225871978124
> > > > 94 29254671108377828505181123363223544733522642
> > > > 95 29422012534394164434460308732785016392648269
> > > > 96 29422234373814288130952278395787210121985088
> > > > 97 35272968574463393967341534160461585917382646
> > > > 98 353119159309222748831313243856786910324359176
> > > > 99 6625510238553543665356603472184747883193878950
> > > > 100 66537588949052664487806404194674003171241776300
> > > > 101 79506266666228385660397674388205519548175533777
> > > > 102 83460774652346563204638264285762372582800370256
> > > > 103 83500464857645127747100048111892035950752300961
> > > > 104 1565954897459587822243928699538705235310483333290
> > > > 105 15659550429333903717991555289114427979545007205655
> > > > 106 18791471864979140528960093801267656715967948563553
> > > > 107 19071825580325395611510184497484555342584143559391
> > > > 108 375768499395186944884167152627327940293807527174416
> > > > 109 3525872593173130742025999658012162159712197258937790
> > > > 110 3525875775502446328379055925379468146399680995144116
> > > > 111 3757694205433918007572957751384864055700332292401865
> > > > 112 4509231204190145510733036220204582129328573161475719
> > > > 113 35460633276294614762040405620969870814838436812830178
> > > > 114 44479150856549293959455344320743473061806660208444238
> > > > 115 45099331914085273661002664687825878143331107837041946
> > > > 116 833344384970448082268284133883858271855565376536904925
> > > > 117
> > > > 8349080332155624231713081083179492935904959634502092369
> > > > 118
> > > > 8494494736061765629427426555355265195335284248206872974
> > > > 119
> > > > 10149204002153390108547890487889270916823079575933962362
> > > > 120
> > > > 10164651772299131805213650116429654236641864328793747363
> > > > 121
> > > > 10164839885301212639303071505650840159892648796514847647
> > > > 122
> > > > 199956775744804225809847377712395449352574301764377579223
> > > > 123
> > > > 1886972414281086161674511177845304507257723547527431000285
> > > > 124
> > > > 1888217142153935558097346285375482726769867588241278181304
> > > > 125
> > > > 1999995439502583265898674445934048845412370233028682938809
> > > > 126
> > > > 2399618691265098587085858994596446709552270253426291952613
> > > > 127
> > > > 2403412387509693362150953011662126428790840099293637798094
> > > > 128
> > > > 24034123877412959297876491276569150818936995200601362450931
> > > > 129
> > > > 24034128950127786743978944250038846932847775561008056870715
> > > > 130
> > > > 444094475816314084600446014682157484565977388194190517154139
> > > > 131
> > > > 444127812333141259185849532528587905684619413078449520063818
> > > > 132
> > > > 452869708646336445787856738547462453605814093477665376368139
> > > > 133
> > > > 4528698044805030262146961546515152445691801354770133610758071
> > > > 134
> > > > 5409278308607726204480539920626390078243376795812851924848744
> > > > 135
> > > > 5434447601212764248913309579030523657334625107149836412782214
> > > > 136
> > > > 5682368436162955753338266813570913161944819309416574459281885
> > > > 137
> > > > 106566315893543295473382540597507299951691746317618589153831038
> > > > 138
> > > > 1006243404664261524895856153709914542801149244957951061819193994
> > > > 139
> > > > 1065679489868692569812289479083957570614889941720405542055383113
> > > > 140
> > > > 1278795890566583557352846249634698150421951034187761931064746944
> > > > 141
> > > >
> 12845209557749430887825155528716606937636114751889126105183316498
> > > > 142
> > > >
> 236350019521823067045893476162647119503126232007609365745929495541
> > > > 143
> > > >
> 240996775255200546547811319941221402418706474191350533243604576597
> > > > 144
> > > >
> 241044886477832495800111281685953839457418627512768010238970273085
> > > > 8
> > > > 145
> > > >
> 242382024471144710299108063596567787329835256370553502007553049453
> > > > 2
> > > > 146
> > > >
> 242383794286767861517360375533556222218246746722488546700951936070
> > > > 1
> > > > 147
> > > >
> 289212099056682396049940959079256609691598864057868919440449999545
> > > > 6
> > > > 148
> > > >
> 289653400053977632477247442251227031909147429684925773070555360792
> > > > 3
> > > > 149
> > > >
> 302687635101758160939417043125197414815348528915726921321932002836
> > > > 6
> > >
> > > > 150
> > > >
> 302832526227732614726159481622269190640865985310518268405350183531
> > > > 6
> > > > 151
> > > >
> 567105814683074601167585367691891750923668018257288252810683666693
> > > > 15
> > > > 152
> > > >
> 567110592090386458193175629928945856101368258056695781526059214536
> > > > 26
> > > > 153
> > > >
> > >
> 53548889192477778779454603709360327203384714533253098739261121817938
> > > 6
> > > > 154
> > > >
> > >
> 57044487820210477188604778388276911487020913766292573068222216337942
> > > 8
> > > > 155
> > > >
> > >
> 68377921181210462308003846263764639830745824354145841031794401990985
> > > 6
> > > > 156
> > > >
> > >
> 68453427902562410968346369402643355316902470492280564132566649081243
> > > 06
> > > > 157
> > > >
> > >
> 68485095908948655929995510453919075038657277188567551800226940503102
> > > 76
> > > > 158
> > > >
> > >
> 12843087774647335193811744652080425992455398427268676794655608666807
> > > 47
> > > > 73
> > > > 159
> > > >
> > >
> 12898757102868462207302705868007693534348569626816161999545317308416
> > > 38
> > > > 872
> > > > 160
> > > >
> > >
> 15414285438207948891863633633134509081926137948447704101253777806397
> > > 54
> > > > 202
> > > > 161
> > > >
> > >
> 16186805674530335853707908387271799011472777859638018203809742597081
> > > 93
> > > > 425
> > > > 162
> > > >
> > >
> 30354960662279826495293525400172720191078056578067591497274461518143
> > > 58
> > > > 5049
> > > > 163
> > > >
> > >
> 30357022929186785333168826367345444430111107806082465682743669135014
> > > 15
> > > > 23956
> > > > 164
> > > >
> > >
> 30413516171223910526679259722962690332166018841560490148274549944948
> > > 36
> > > > 57596
> > > > 165
> > > >
> > >
> 36445255767533170031769539348749684277174212742307626062837744737816
> > > 90
> > > > 72321
> > > > 166
> > > >
> > >
> 36975575590791450134172879969442837760425914765427227582789490580843
> > > 07
> > > > 83491
> > > > 167
> > > >
> > >
> 72840092146241749647474764368087771811048364023125336822239991434320
> > > 21
> > > > 825922
> > > > 168
> > > >
> > >
> 68360567907743212453951196753935278021975426889350236521694123385869
> > > 40
> > > > 0106816
> > > > 169
> > > >
> > >
> 68779193834334390117024504968502062432224578910274283033617432192213
> > > 71
> > > > 9890984
> > > > 170
> > > >
> > >
> 72855187850312769815357362080933787676996145344041301790567304091791
> > > 98
> > > > 0766762
> > > > 171
> > > >
> > >
> 87423160586792607271064891572590141379028387768831255960472469769559
> > > 92
> > > > 3418837
> > > > 172
> > > >
> > >
> 68738435612073418766881760082006836981887651256215505155727900491363
> > > 92
> > > > 14364760
> > > > 173
> > > >
> > >
> 68779360404390478686760481763982822334335310012707867402083361316612
> > > 46
> > > > 64587675
> > > > 174
> > > >
> > >
> 86260982466762712975306234187420241107087185470231545128478524700092
> > > 02
> > > > 13599774
> > > > 175
> > > >
> > >
> 87426225422912632175787218790314917654595008145058231053353633460881
> > > 36
> > > > 09783293
> > > > 176
> > > >
> > >
> 16154985722751193229440139509826011884938733121741314227180871821697
> > > 67
> > > > 4607557307
> > > > 177
> > > >
> > >
> 16184941752388841501380962827503903747084836652306194990502294903037
> > > 63
> > > > 29697510206
> > > > 178
> > > >
> > >
> 16467160395194102227277339744002130816761581968042412654647392271915
> > > 52
> > > > 42424855152
> > > > 179
> > > >
> > >
> 19704551355009461908202294172679464397068919657705987745962653487867
> > > 95
> > > > 27146493573
> > > > 180
> > > >
> > >
> 38763081440277244806593698569931722821303005075665143687855733137893
> > > 28
> > > > 238576805195
> > > > 181
> > > >
> > >
> 36601798104385958018085863830734653034028333394017955317633786397281
> > > 55
> > > > 0417127279081
> > > > 182
> > > >
> > >
> 38768441223546473806693057761791216722610791228839898732769875819037
> > > 60
> > > > 5973370456405
> > > > 183
> > > >
> > >
> 46588444484103329777392745326636167632868999625633785864312018197167
> > > 32
> > > > 5373681927853
> > > > 184
> > > >
> > >
> 46590841632219940774444592276892495432532365602383541583254483410510
> > > 74
> > > > 55690921039246
> > > > 185
> > > >
> > >
> 86090913485180968379154488388734879790120179109712233145326733002235
> > > 23
> > > > 214106226101895
> > > > 186
> > > >
> > >
> 87789932407487685803701525950803383941547353788723161985711232649982
> > > 70
> > > > 707468972868034
> > > > 187
> > > >
> > >
> 87791872827571237040947018005583367341858529935979219463583588969784
> > > 72
> > > > 3209865390258652
> > > > 188
> > > >
> > >
> 10486091509916774967713804927595595501585933674177231277134808813955
> > > 65
> > > > 03040215197174655
> > > > 189
> > > >
> > >
> 10534857252108188279626135662109132797245842165847824749060017499844
> > > 34
> > > > 07727153799368471
> > > > 190
> > > >
> > >
> 11015413671575651442583821549363378981317023007366120753361236443103
> > > 67
> > > > 01405737675065877
> > > > 191
> > > >
> > >
> 20657097255621747930380443252330202034468054166794190206726989984038
> > > 73
> > > > 426042914402300023
> > > > 192
> > > >
> > >
> 19505480371218974183326888803180534389620164706936547103782818904411
> > > 29
> > > > 2526999464062269840
> > > > 193
> > > >
> > >
> 20669923950116346189855699316290717912368841544110261847521071096365
> > > 14
> > > > 7226901298980626197
> > > > 194
> > > >
> > >
> 20670394820428551278544297233503165118248146909466983323560891683812
> > > 60
> > > > 6114228953976474713
> > > > 195
> > > >
> > >
> 24792784120791372125801822447150291468261682308711557228213891031045
> > > 88
> > > > 2163703213202104702
> > > > 196
> > > >
> > >
> 24911084425205453941560048507440823724439731248255102863223416742970
> > > 48
> > > > 2583936227794366302
> > > > 197
> > > >
> > >
> 24911220632872794655267956395354021999777405555324505263501015359243
> > > 81
> > > > 83431271736900797559
> > > > 198
> > > >
> > >
> 45814837841693129752194740236561633827974815580250237982803411026593
> > > 15
> > > > 924552715806523021070
> > > > 199
> > > >
> > >
> 46718890779103462034384179438860619876433441388067756881156460113444
> > > 96
> > > > 591316074349424314863
> > > > 200
> > > >
> > >
> 46728187962820269751508178020959160548288458652554354369409966740497
> > > 17
> > > > 3369690347576875351029
> > > > 201
> > > >
> > >
> 46987407442996837200375255383811870384851392565607086036490029614261
> > > 63
> > > > 9901308294691109067975
> > > > 202
> > > >
> > >
> 56150349612989490742972479251658638217026724885944848154838327293543
> > > 09
> > > > 4899837715349660322931
> > > > 203
> > > >
> > >
> 58704957378199363664224748489325536449316711005896105890024162686437
> > > 61
> > > > 6409749978253100310285
> > > > 204
> > > >
> > >
> 10993022084006088518858311630528712468619280025564873120858470361203
> > > 81
> > > > 947495855110877218079259
> > > > 205
> > > >
> > >
> 10382344998448994615505358708522747718458015979471799397598232413954
> > > 22
> > > > 3393598785871875214072624
> > > > 206
> > > >
> > >
> 11058238755734969016823372772691799155079119171166396314484223520322
> > > 48
> > > > 4229379109183145902150085
> > > > 207
> > > >
> > >
> 13256766685413566705858917740617552721986970094161234538850925837777
> > > 53
> > > > 1135766641904506038365621
> > > > 208
> > > >
> > >
> 13276032559225131249500718043197071092020399554241912179426648078584
> > > 62
> > > > 54023458862130847944510919
> > > >
> > > > _______________________________________________
> > > >
> > > > Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > >
> > >
> > >
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> Here it is the code in PARI-GP:
>
> ct=1;print("1 0");for(L=1,200,pos=1;a=vector(L);a[1]=0;\
> while(pos>0,backtrack=0;a[pos]++;\
> if(a[pos]>1,backtrack=1,\
> n1=sum(i=1,pos,a[i]*3^(L-i));n2=n1+3^(L-pos);n=sum(i=1,L,a[i]*
> 2^(L-i));\
> if(pos==L,L1=length(binary(n1));\
> if(shift(n1,L-L1)==n,ct++;print(ct" "n1)),\
> b1=binary(n1);b2=binary(n2);L1=length(b1);L2=length(b2);ext=1;\
> if(L1==L2,s=0;while(s+1<=L1&&s+1<=pos&&b1[s+1]==b2[s+1],s++);\
> if(sum(i=1,s,abs(b1[i]-a[i]))!=0,ext=0));if(ext,pos++;a[pos]=-1)));\
> if(backtrack,pos--)))
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
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