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A033203 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. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

MATHEMATICA

QuadPrimes[1, 0, 2, 10000] (* see A106856 *)

Select[Prime[Range[200]], MemberQ[{1, 2, 3}, Mod[#, 8]]&] (* Harvey P. Dale, Mar 16 2013 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 16 06:51 EDT 2014. Contains 240552 sequences.