Prime-Generating Binary Sequences Based on Prime-Indexed Zeros

[Ali Sada]

Hi everyone,

Happy New Year. 

I got this idea for these sequences from a comment by Daniel in a previous email. In binary, start with two 1s and fill the intervening positions with 0s at prime-indexed positions and 1s elsewhere. We get two different sequences based on whether we count the positions from the right or the left. In both cases, some of these numbers are primes
Counting from the right: the 1st (5), 3rd (41), 6th (11177), 12th (204811725737), and 48th (20218313985789220934578265728514876480355276692856785622098635320233) terms are primes.
Counting from the left, the 1st (5), 3rd (37), 4th (149), 7th (153437), 10th (628479869), and 21st (11056334789265976156021) are primes.

I would really appreciate it if you could tell me if these two sequences (and the initial sequences below) are suitable for the OEIS. Also, please help confirm the terms. 

Best,

Ali 

Initial sequences

Counting from the right 

5
9
41
169
2985
11177
191401
715689
12250025
800779177
2948262825
204811725737
3228468702121
12024561724329
205538608212905
13434862513613737
860111592459266985
3165954601672960937
219915197467760192425
3466542154440641276841
12911275120179931704233
900716173899673231879081
14198900189660594153647017
923311116539861733532691369
237369858620047494239265418153
3723409009247678348355199232937
13864613811073513560328824875945
236971119451241888223748589022121
886008226768095341790060630174633
15164824587738871320248925535529897
255206170827857447158337082514044808105
3998312206958180545255457764263495134121
259890652131503905069713162552953190149033
956788939585585878242704358573214487210921
1069998761894147332725611199053654044180147113
3924494147306067094842183137952644316945640361
272247060376026524733799945394457729956902005673
17444891299014135813627096729810783210914109385641
274669179469253049417475627287876594670358236949417
17859456879834676961244211534530193887170538594036649
1143285869703221807318155309598038500607182081447619497
4208276951434999524034849363898656867844660325814823849
4705904596327982016967443528661047232210136287185106299817
17260108067101343544639022375076380064414847176113175325609
293452584424115297153413756996213702372918486732530693893033
1096921606553610434924394803166795003634019983623927111543721
4936003655525912746624289980382877147349319413890580724322069417
20218313985789220934578265728514876480355276692856785622098635320233
316777727324446258675915431685730813890363865340803082914238348061609
1179496020673266732105259914470358995446752486862101402309553876036521

Counting from the left 

5
9
37
149
2397
9589
153437
613749
9819997
628479869
2513919477
160890846589
2574253545437
10297014181749
164752226907997
10544142522111869
674825121415159677
2699300485660638709
172755231082280877437
2764083697316494039005
11056334789265976156021
707605426513022473985405
11321686824208359583766493
724587956749335013361055613
185494516927829763420430237181
2967912270845276214726883794909
11871649083381104858907535179637
189946385334097677742520562874205
759785541336390710970082251496821
12156568661382251375521316023949149
199173220948086806536541241736382873597
3186771535169388904584659867782125977565
203953378250840889893418231538056062564221
815813513003363559573672926152224250256885
835393037315444285003441076379877632263051261
3341572149261777140013764305519510529052205045
213860617552753736960880915553248673859341122941
13687079523376239165496378595407915126997831868285
218993272374019826647942057526526642031965309892573
14015569431937268905468291681697705090045779833124733
896996443643985209949970667628653125762929909319982973
3587985774575940839799882670514612503051719637279931893
3674097433165763419955079854606963203124960908574650259453
14696389732663053679820319418427852812499843634298601037813
235142235722608858877125110694845644999997498148777616605021
940568942890435435508500442779382579999989992595110466420085
3852570390079223543842817813624351047679959009669572470456672253
15780128317764499635580181764605341891297112103606568838990529552381
252482053084231994169282908233685470260753793657705101423848472838109
1009928212336927976677131632934741881043015174630820405695393891352437

[Kevin Ryde]

Ali Sada <ali....@gmail.com> writes:
>
> 204811725737

That sort of thing is for instance A176496 = sum 2^not_prime.
That sequence sticks to the "indexing" so the term there is
2* what you have.

A076793 = sum 2^prime is the sort of likely thing to look for,
and hope that it may lead off to variations.

[Ali Sada]

Thank you, Kevin!

Best,

Ali

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