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A139513
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Primes congruent to {1, 3, 7, 9} mod 20.
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15
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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
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OFFSET
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1,1
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COMMENTS
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Rational primes that decompose in the field Q(sqrt(-5)). - N. J. A. Sloane, Dec 25 2017
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REFERENCES
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Dirichlet & Dedekind, Lectures on Number Theory (English Translation 1999), p. 119.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(700) | p mod 20 in [1, 3, 7, 9] ]; // Vincenzo Librandi, Aug 15 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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