A003626 Inert rational primes in Q(sqrt(-5)). (Formerly M4769)

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

1,1

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

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A139513.

Sequence in context: A045798 A267277 A155071 * A154981 A092912 A092911

Adjacent sequences: A003623 A003624 A003625 * A003627 A003628 A003629

Keyword

nonn,nice

Author

N. J. A. Sloane, Mira Bernstein

Status

approved