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A033203
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Primes congruent to {1, 2, 3} mod 8; or primes of form x^2+2*y^2; or primes p such that x^2 = -2 has a solution mod p.
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19
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2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193, 211, 227, 233, 241, 251, 257, 281, 283, 307, 313, 331, 337, 347, 353, 379, 401, 409, 419, 433, 443, 449, 457, 467, 491, 499, 521, 523
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OFFSET
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1,1
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COMMENTS
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Sequence naturally partitions into two sequences: *all* primes p with ord_p(-2) odd (A163183)[ = the primes dividing 2^j +1 for some odd j] and certain primes p with ord_p(-2) even (A163185). [From Christopher J. Smyth, Jul 23 2009]
Terms m in A047476 with A010051(m) = 1. - Reinhard Zumkeller, Dec 29 2012
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REFERENCES
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D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
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QuadPrimes[1, 0, 2, 10000] (* see A106856 *)
Select[Prime[Range[200]], MemberQ[{1, 2, 3}, Mod[#, 8]]&] (* Harvey P. Dale, Mar 16 2013 *)
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PROG
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(Haskell)
a033203 n = a033203_list !! (n-1)
a033203_list = filter ((== 1) . a010051) a047476_list
-- Reinhard Zumkeller, Dec 29 2012, Jan 22 2012
(MAGMA) [p: p in PrimesUpTo(600) | p mod 8 in [1..3]]; // Vincenzo Librandi, Aug 11 2012
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CROSSREFS
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Cf. A033200.
Cf. A039706, A003628 (complement with respect to A000040).
Sequence in context: A091734 A038902 A019355 * A051100 A051088 A051092
Adjacent sequences: A033200 A033201 A033202 * A033204 A033205 A033206
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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