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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
2, 19, 3, 173, 53, 523, 31883, 123637, 71899, 565589, 1241557, 1925501, 604829, 52003139, 410665589, 3448332373, 1250481059, 5352930581 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(17) from Martin Ehrenstein, Dec 21 2022
STATUS
approved

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Last modified April 13 12:42 EDT 2024. Contains 371641 sequences. (Running on oeis4.)