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A139513 Primes congruent to {1, 3, 7, 9} mod 20. 15
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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A032403 A072584 A262250 * A144593 A057191 A090548
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Apr 25 2008
STATUS
approved

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Last modified March 19 06:56 EDT 2024. Contains 370953 sequences. (Running on oeis4.)