A140002 - OEIS

A140002

Primes of the form 8*x^2 + 165*y^2.

173, 197, 293, 557, 677, 1493, 1613, 1733, 1877, 1997, 2213, 2477, 2837, 3533, 3797, 4133, 4157, 4253, 4373, 4397, 4517, 4637, 5477, 5573, 5693, 5717, 6173, 7013, 7757, 7853, 8093, 8117, 8597, 9173, 9413, 9437, 9533, 9677, 10133, 10733

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OFFSET

1,1

COMMENTS

Discriminant = -5280. See A139827 for more information.

LINKS

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

FORMULA

The primes are congruent to {173, 197, 293, 413, 437, 557, 677, 893, 1157, 1253} (mod 1320).

MATHEMATICA

QuadPrimes2[8, 0, 165, 10000] (* see A106856 *)

PROG

(PARI) isA140002(n) = if(isprime(n), {r=0; for(y=0, floor(sqrt(n/165)), t=n-165*y^2; if((t%8==0)&(issquare(t/8)), r=1)); r}, 0) \\ Michael B. Porter, Oct 05 2009

(Magma) [p: p in PrimesUpTo(12000) | p mod 1320 in [173, 197, 293, 413, 437, 557, 677, 893, 1157, 1253]]; // Vincenzo Librandi, Aug 04 2012

CROSSREFS

Sequence in context: A364937 A261530 A246135 * A178652 A119567 A142436

Adjacent sequences: A139999 A140000 A140001 * A140003 A140004 A140005

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 02 2008

STATUS

approved