The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A358980 Least prime in a string of exactly n consecutive primes with primitive root 2, or 0 if no such prime exists. 0

%I #33 Mar 21 2024 14:41:21

%S 2,19,3,173,53,523,31883,123637,71899,565589,1241557,1925501,604829,

%T 52003139,410665589,3448332373,1250481059,5352930581

%N Least prime in a string of exactly n consecutive primes with primitive root 2, or 0 if no such prime exists.

%C Pollack shows, on GRH, that arbitrarily large members of this sequence exist. This works with any nonsquare primitive root aside from -1. - _Charles R Greathouse IV_, Mar 21 2024

%H Paul Pollack, <a href="https://arxiv.org/abs/1404.4007">Bounded gaps between primes with a given primitive root</a> arXiv:1404.4007 [math.NT], 2014.

%e a(5) = 523 because 523 is the least prime in a string of 5 consecutive primes, {523, 541, 547, 557, 563} all having 2 as primitive root.

%t Table[p=2;While[(k=0;While[PrimitiveRoot@p==2,k++;p=NextPrime[p]];k)!=n, p=NextPrime@p];NextPrime[p,-k],{n,0,9}]

%Y Cf. A001122.

%K nonn,more

%O 0,1

%A _Giorgos Kalogeropoulos_, Dec 12 2022

%E a(17) from _Martin Ehrenstein_, Dec 21 2022

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 16:44 EDT 2024. Contains 372801 sequences. (Running on oeis4.)