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A033203
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Primes p congruent to {1, 2, 3} (mod 8); or primes p of form x^2 + 2*y^2; or primes p such that x^2 = -2 has a solution mod p.
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26
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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, 547, 563, 569, 571, 577, 587, 593, 601, 617, 619, 641, 643, 659, 673, 683
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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). - Christopher J. Smyth, Jul 23 2009
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REFERENCES
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David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.
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LINKS
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FORMULA
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MATHEMATICA
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QuadPrimes2[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
(Magma) [p: p in PrimesUpTo(600) | p mod 8 in [1..3]]; // Vincenzo Librandi, Aug 11 2012
(Magma) [p: p in PrimesUpTo(800) | NormEquation(2, p) eq true]; // Bruno Berselli, Jul 03 2016
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CROSSREFS
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Cf. A051100 (see Mathar's comment).
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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