A358980 Least prime in a string of exactly n consecutive primes with primitive root 2, or 0 if no such prime exists.

2, 19, 3, 173, 53, 523, 31883, 123637, 71899, 565589, 1241557, 1925501, 604829, 52003139, 410665589, 3448332373, 1250481059, 5352930581

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..17.

Paul Pollack, Bounded gaps between primes with a given primitive root arXiv:1404.4007 [math.NT], 2014.

Example

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.

Mathematica

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}]

Crossrefs

Cf. A001122.

Sequence in context: A221229 A221602 A354207 * A092120 A059706 A370387

Adjacent sequences: A358977 A358978 A358979 * A358981 A358982 A358983

Keyword

nonn,more

Author

Giorgos Kalogeropoulos, Dec 12 2022

Extensions

a(17) from Martin Ehrenstein, Dec 21 2022

Status

approved