A003632 Inert rational primes in Q(sqrt 7), or, 7 is not a square mod p.

5, 11, 13, 17, 23, 41, 43, 61, 67, 71, 73, 79, 89, 97, 101, 107, 127, 151, 157, 163, 173, 179, 181, 191, 211, 229, 239, 241, 257, 263, 269, 293, 313, 331, 347, 349, 353, 359, 379, 397, 409, 431, 433, 443, 461, 463, 487, 491, 499, 509, 521, 547, 571, 577, 593, 599

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Comments

Primes congruent to 5, 11, 13, 15, 17, 23 (modulo 28). - Michael Somos, Aug 14 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

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index to sequences related to decomposition of primes in quadratic fields

Programs

Mathematica

Select[Prime[Range[1000]],MemberQ[{5,11,13,15,17,23},Mod[#,28]]&] (* Vincenzo Librandi, Aug 20 2012 *)

PARI

{a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( 7, m )== -1, cnt++ )); m} /* Michael Somos, Aug 14 2012 */