A003626 Inert rational primes in Q(sqrt(-5)).

11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 211, 233, 239, 251, 257, 271, 277, 293, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 419, 431, 433, 439, 457, 479, 491, 499, 557, 571, 577, 593, 599

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• nice

Comments

Primes congruent to 11, 13, 17, 19 (mod 20). - Michael Somos, Aug 14 2012

Legendre symbol (-5, a(n)) = -1. For prime 5 this symbol is set to 0, and for other odd primes (-5, prime) = +1, given in A139513. - Wolfdieter Lang, Mar 05 2021

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
• R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 1993
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A139513.

Programs

Mathematica

Select[Prime[Range[1000]],MemberQ[{11,13,17,19},Mod[#,20]]&] (* Vincenzo Librandi, Aug 20 2012 *)

PARI

{a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( -20, m )==-1, cnt++ )); m} /* Michael Somos, Aug 14 2012 */