A127807 - OEIS

%I #8 Apr 28 2020 22:22:19

%S 3,2,2,3,2,2,3,2,5,2,3,2,6,3,5,2,2,2,2,7,5,3,2,3,5,2,5,2,6,3,3,2,3,2,

%T 2,6,5,2,5,2,2,2,19,5,2,3,2,3,2,6,3,7,7,6,3,5,2,6,5,3,3,2,5,17,10,2,3,

%U 10,2,2,3,7,6,2,2,5,2,5,3,21,2,2,7,5,15,2,3,13,2,3,2,13,3,2,7,5,2,3,2,2

%N Least positive primitive root of (n-th prime)^2.

%C A055578 lists the indices n such that a(n) differs from A001918(n).

%D D. Cohen, R. W. K. Odoni, and W. W. Stothers, On the Least Primitive Root Modulo p^2, Bulletin of the London Mathematical Society 6:1 (March 1974), pp. 42-46.

%H Bryce Kerr, Kevin McGown, and Tim Trudgian, <a href="https://arxiv.org/abs/1908.11497">The least primitive root modulo p^2</a>. arXiv:1908.11497 [math.NT]

%F Cohen, Odoni, & Stothers prove that a(n) < prime(n)^(1/4 + e) for any e > 0 and all large enough n. Kerr, McGown, & Trudgian give an effective version: a(n) < prime(n)^0.99 for all n. - _Charles R Greathouse IV_, Apr 28 2020

%t << NumberTheory`NumberTheoryFunctions` Table[PrimitiveRoot[(Prime[n])^2], {n, 1, 100}]

%t PrimitiveRoot[Prime[Range[100]]^2] (* _Harvey P. Dale_, Aug 19 2017 *)

%Y Cf. A001918, A127808, A127809, A127810.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Jan 29 2007