A139513 Primes congruent to {1, 3, 7, 9} mod 20.

3, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 103, 107, 109, 127, 149, 163, 167, 181, 223, 227, 229, 241, 263, 269, 281, 283, 307, 347, 349, 367, 383, 389, 401, 409, 421, 443, 449, 461, 463, 467, 487, 503, 509, 521, 523, 541, 547, 563, 569, 587, 601, 607, 641

Offset

1,1

Comments

Rational primes that decompose in the field Q(sqrt(-5)). - N. J. A. Sloane, Dec 25 2017

References

Dirichlet & Dedekind, Lectures on Number Theory (English Translation 1999), p. 119.

David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989, p. 14 (1.8), p. 32 (2.19).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Nov 29 2016

Legendre symbol (-5, a(n)) = +1. One sets (-5, 5) = 0 and for odd primes p == -1, -3, -7, -9 (mod 20) (-5, p) = -1, given in A003626. - Wolfdieter Lang, Mar 05 2021

Mathematica

a = {}; Do[If[MemberQ[{1, 3, 7, 9}, Mod[Prime[n], 20]], AppendTo[a, Prime[n]]], {n, 1, 200}]; a (*Artur Jasinski*)
Select[Prime[Range[200]], MemberQ[{1, 3, 7, 9}, Mod[#, 20]]&] (* Vincenzo Librandi, Aug 15 2012 *)

Prog

(Magma) [ p: p in PrimesUpTo(700) | p mod 20 in [1, 3, 7, 9] ]; // Vincenzo Librandi, Aug 15 2012
(PARI) select(p->my(k=p%20); k==1 || k==3 || k==7 || k==9, primes(100)) \\ Charles R Greathouse IV, Nov 29 2016

Crossrefs

Cf. A296922, A003626.

Sequence in context: A032403 A072584 A262250 * A144593 A057191 A090548

Adjacent sequences: A139510 A139511 A139512 * A139514 A139515 A139516

Keyword

nonn,easy

Author

Artur Jasinski, Apr 25 2008

Status

approved