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A003630 Inert rational primes in Q(sqrt 3).
(Formerly M3766)
4
5, 7, 17, 19, 29, 31, 41, 43, 53, 67, 79, 89, 101, 103, 113, 127, 137, 139, 149, 151, 163, 173, 197, 199, 211, 223, 233, 257, 269, 271, 281, 283, 293, 307, 317, 331, 353, 367, 379, 389, 401, 439, 449, 461, 463, 487, 499, 509, 521, 523, 547, 557, 569, 571, 593 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that p divides 3^(p-1)/2 + 1. - Cino Hilliard, Sep 04 2004

Primes p such that 1+4*x+x^2 is irreducible over GF(p). [Joerg Arndt, Aug 10 2011]

Conjecture: Primes congruent to (5, 7) mod 12. - Vincenzo Librandi, Aug 06 2012

REFERENCES

H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 498.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

PROG

(PARI) {a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( 12, m )== -1, cnt++ )); m} /* Michael Somos, Aug 14 2012 */

CROSSREFS

Sequence in context: A099382 A163633 A092242 * A122565 A247607 A079016

Adjacent sequences:  A003627 A003628 A003629 * A003631 A003632 A003633

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified March 23 04:20 EDT 2017. Contains 283902 sequences.