[seqfan] Re: "summer hours" NEW SEQ Z1

Fri Jun 4 14:56:13 CEST 2010

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
> > > >
> > > >
> > >
> > 14392731189,15114438648,283004031766,283592574694,2672433464707,283593
> > > 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}];(*Ray
> > > > 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
> > > 2410448864778324958001112816859538394574186275127680102389702730858
> > > 145
> > > 2423820244711447102991080635965677873298352563705535020075530494532
> > > 146
> > > 2423837942867678615173603755335562222182467467224885467009519360701
> > > 147
> > > 2892120990566823960499409590792566096915988640578689194404499995456
> > > 148
> > > 2896534000539776324772474422512270319091474296849257730705553607923
> > > 149
> > > 3026876351017581609394170431251974148153485289157269213219320028366
> >
> > > 150
> > > 3028325262277326147261594816222691906408659853105182684053501835316
> > > 151
> > > 56710581468307460116758536769189175092366801825728825281068366669315
> > > 152
> > > 56711059209038645819317562992894585610136825805669578152605921453626
> > > 153
> > >
> > 535488891924777787794546037093603272033847145332530987392611218179386
> > > 154
> > >
> > 570444878202104771886047783882769114870209137662925730682222163379428
> > > 155
> > >
> > 683779211812104623080038462637646398307458243541458410317944019909856
> > > 156
> > >
> > 6845342790256241096834636940264335531690247049228056413256664908124306
> > > 157
> > >
> > 6848509590894865592999551045391907503865727718856755180022694050310276
> > > 158
> > >
> > 1284308777464733519381174465208042599245539842726867679465560866680747
> > > 73
> > > 159
> > >
> > 1289875710286846220730270586800769353434856962681616199954531730841638
> > > 872
> > > 160
> > >
> > 1541428543820794889186363363313450908192613794844770410125377780639754
> > > 202
> > > 161
> > >
> > 1618680567453033585370790838727179901147277785963801820380974259708193
> > > 425
> > > 162
> > >
> > 3035496066227982649529352540017272019107805657806759149727446151814358
> > > 5049
> > > 163
> > >
> > 3035702292918678533316882636734544443011110780608246568274366913501415
> > > 23956
> > > 164
> > >
> > 3041351617122391052667925972296269033216601884156049014827454994494836
> > > 57596
> > > 165
> > >
> > 3644525576753317003176953934874968427717421274230762606283774473781690
> > > 72321
> > > 166
> > >
> > 3697557559079145013417287996944283776042591476542722758278949058084307
> > > 83491
> > > 167
> > >
> > 7284009214624174964747476436808777181104836402312533682223999143432021
> > > 825922
> > > 168
> > >
> > 6836056790774321245395119675393527802197542688935023652169412338586940
> > > 0106816
> > > 169
> > >
> > 6877919383433439011702450496850206243222457891027428303361743219221371
> > > 9890984
> > > 170
> > >
> > 7285518785031276981535736208093378767699614534404130179056730409179198
> > > 0766762
> > > 171
> > >
> > 8742316058679260727106489157259014137902838776883125596047246976955992
> > > 3418837
> > > 172
> > >
> > 6873843561207341876688176008200683698188765125621550515572790049136392
> > > 14364760
> > > 173
> > >
> > 6877936040439047868676048176398282233433531001270786740208336131661246
> > > 64587675
> > > 174
> > >
> > 8626098246676271297530623418742024110708718547023154512847852470009202
> > > 13599774
> > > 175
> > >
> > 8742622542291263217578721879031491765459500814505823105335363346088136
> > > 09783293
> > > 176
> > >
> > 1615498572275119322944013950982601188493873312174131422718087182169767
> > > 4607557307
> > > 177
> > >
> > 1618494175238884150138096282750390374708483665230619499050229490303763
> > > 29697510206
> > > 178
> > >
> > 1646716039519410222727733974400213081676158196804241265464739227191552
> > > 42424855152
> > > 179
> > >
> > 1970455135500946190820229417267946439706891965770598774596265348786795
> > > 27146493573
> > > 180
> > >
> > 3876308144027724480659369856993172282130300507566514368785573313789328
> > > 238576805195
> > > 181
> > >
> > 3660179810438595801808586383073465303402833339401795531763378639728155
> > > 0417127279081
> > > 182
> > >
> > 3876844122354647380669305776179121672261079122883989873276987581903760
> > > 5973370456405
> > > 183
> > >
> > 4658844448410332977739274532663616763286899962563378586431201819716732
> > > 5373681927853
> > > 184
> > >
> > 4659084163221994077444459227689249543253236560238354158325448341051074
> > > 55690921039246
> > > 185
> > >
> > 8609091348518096837915448838873487979012017910971223314532673300223523
> > > 214106226101895
> > > 186
> > >
> > 8778993240748768580370152595080338394154735378872316198571123264998270
> > > 707468972868034
> > > 187
> > >
> > 8779187282757123704094701800558336734185852993597921946358358896978472
> > > 3209865390258652
> > > 188
> > >
> > 1048609150991677496771380492759559550158593367417723127713480881395565
> > > 03040215197174655
> > > 189
> > >
> > 1053485725210818827962613566210913279724584216584782474906001749984434
> > > 07727153799368471
> > > 190
> > >
> > 1101541367157565144258382154936337898131702300736612075336123644310367
> > > 01405737675065877
> > > 191
> > >
> > 2065709725562174793038044325233020203446805416679419020672698998403873
> > > 426042914402300023
> > > 192
> > >
> > 1950548037121897418332688880318053438962016470693654710378281890441129
> > > 2526999464062269840
> > > 193
> > >
> > 2066992395011634618985569931629071791236884154411026184752107109636514
> > > 7226901298980626197
> > > 194
> > >
> > 2067039482042855127854429723350316511824814690946698332356089168381260
> > > 6114228953976474713
> > > 195
> > >
> > 2479278412079137212580182244715029146826168230871155722821389103104588
> > > 2163703213202104702
> > > 196
> > >
> > 2491108442520545394156004850744082372443973124825510286322341674297048
> > > 2583936227794366302
> > > 197
> > >
> > 2491122063287279465526795639535402199977740555532450526350101535924381
> > > 83431271736900797559
> > > 198
> > >
> > 4581483784169312975219474023656163382797481558025023798280341102659315
> > > 924552715806523021070
> > > 199
> > >
> > 4671889077910346203438417943886061987643344138806775688115646011344496
> > > 591316074349424314863
> > > 200
> > >
> > 4672818796282026975150817802095916054828845865255435436940996674049717
> > > 3369690347576875351029
> > > 201
> > >
> > 4698740744299683720037525538381187038485139256560708603649002961426163
> > > 9901308294691109067975
> > > 202
> > >
> > 5615034961298949074297247925165863821702672488594484815483832729354309
> > > 4899837715349660322931
> > > 203
> > >
> > 5870495737819936366422474848932553644931671100589610589002416268643761
> > > 6409749978253100310285
> > > 204
> > >
> > 1099302208400608851885831163052871246861928002556487312085847036120381
> > > 947495855110877218079259
> > > 205
> > >
> > 1038234499844899461550535870852274771845801597947179939759823241395422
> > > 3393598785871875214072624
> > > 206
> > >
> > 1105823875573496901682337277269179915507911917116639631448422352032248
> > > 4229379109183145902150085
> > > 207
> > >
> > 1325676668541356670585891774061755272198697009416123453885092583777753
> > > 1135766641904506038365621
> > > 208
> > >
> > 1327603255922513124950071804319707109202039955424191217942664807858462
> > > 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--)))