

A139857


Primes of the form 8x^2 + 15y^2.


4



23, 47, 167, 263, 383, 503, 647, 743, 863, 887, 983, 1103, 1223, 1367, 1487, 1583, 1607, 1823, 1847, 2063, 2087, 2207, 2423, 2447, 2543, 2663, 2687, 2903, 2927, 3023, 3167, 3407, 3527, 3623, 3767, 3863, 4007, 4127, 4463, 4583, 4703, 4943
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OFFSET

1,1


COMMENTS

Discriminant= = 480. See A139827 for more information.
Also primes of the form 12x^2 + 12xy + 23y^2, which has discriminant = 960.  T. D. Noe, May 07 2008
Also primes of the forms 23x^2 + 22xy + 47y^2 and 23x^2 + 8xy + 32y^2. 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 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 {23, 47} (mod 120).


MATHEMATICA

QuadPrimes2[8, 0, 15, 10000] (* see A106856 *)


PROG

(Magma) [ p: p in PrimesUpTo(6000)  p mod 120 in {23, 47}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\8), w=8*x^2; for(y=1, sqrtint((limw)\15), if(isprime(t=w+15*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017


CROSSREFS

Sequence in context: A239563 A241207 A042050 * A139900 A065017 A140618
Adjacent sequences: A139854 A139855 A139856 * A139858 A139859 A139860


KEYWORD

nonn,easy


AUTHOR

T. D. Noe, May 02 2008


STATUS

approved



