A003632 Inert rational primes in Q(sqrt 7), or, 7 is not a square mod p. (Formerly M3806)

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

1,1

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

Mathematica

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

Prog

(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 */

Crossrefs

Sequence in context: A106091 A246374 A040113 * A019354 A230288 A124662

Adjacent sequences: A003629 A003630 A003631 * A003633 A003634 A003635

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Status

approved