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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

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