A094319 Prime values of Lehmer's polynomial 263*x^2+3.

3, 4211, 51551, 177791, 420803, 4043891, 4444703, 4864451, 9898271, 13196291, 16437503, 16967711, 34846451, 37181891, 44210303, 48628703, 56622851, 64181471, 75558851, 82476803, 95946611, 101097203, 107724803, 113178371, 137858291, 140152703, 165804671

Offset

0,1

Comments

For the first 206 primes p assumed by this quadratic form with x>=0, the number 326 is a primitive root modulo p.

References

K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory. Springer-Verlag, NY, 1982, p. 47.

D. H. Lehmer, A note on primitive roots, Scripta Math., 26 1963 117-119.

Pieter Moree, Posting to Number Theory List, Jun 03, 2004.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Pieter Moree, Primitive root producing quadratics, arXiv:math/0406033 [math.NT], 2004.

Maple

P:= x -> 263*x^2+3:
select(isprime, map(P, [$0..1000])); # Robert Israel, Feb 01 2021

Mathematica

Select[Table[263*x^2+3, {x, 0, 800}], PrimeQ] (* Harvey P. Dale, Dec 04 2015 *)

Crossrefs

Cf. A094320.

Sequence in context: A116213 A136544 A024048 * A362536 A229766 A003166

Adjacent sequences: A094316 A094317 A094318 * A094320 A094321 A094322

Keyword

nonn

Author

N. J. A. Sloane, Jun 03 2004

Status

approved