A139855 - OEIS

A139855

Primes of the form 4x^2+4xy+31y^2.

31, 79, 151, 199, 271, 439, 631, 751, 919, 991, 1039, 1231, 1279, 1399, 1471, 1759, 1831, 1879, 1951, 1999, 2239, 2311, 2551, 2671, 2719, 2791, 3079, 3271, 3319, 3391, 3511, 3559, 3631, 3919, 4111, 4159, 4231, 4519, 4591, 4639, 4759, 4831

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OFFSET

1,1

COMMENTS

Discriminant = -480. See A139827 for more information.

Also primes of the form 15x^2+16y^2, which has discriminant = -960. - T. D. Noe, May 07 2008

Also primes of the form 16x^2+8xy+31y^2, which has discriminant = -1920. See A140633. - T. D. Noe, May 19 2008

LINKS

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

William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See item 14 in Table II.

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

FORMULA

The primes are congruent to {31, 79} (mod 120).

MATHEMATICA

QuadPrimes2[4, -4, 31, 10000] (* see A106856 *)

PROG

(Magma) [ p: p in PrimesUpTo(6000) | p mod 120 in {31, 79}]; // Vincenzo Librandi, Jul 29 2012

CROSSREFS

Sequence in context: A142408 A246929 A033220 * A139901 A242777 A252231

Adjacent sequences: A139852 A139853 A139854 * A139856 A139857 A139858

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 02 2008

STATUS

approved