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A107007 Primes of the form 3*x^2+8*y^2. 6
3, 11, 59, 83, 107, 131, 179, 227, 251, 347, 419, 443, 467, 491, 563, 587, 659, 683, 827, 947, 971, 1019, 1091, 1163, 1187, 1259, 1283, 1307, 1427, 1451, 1499, 1523, 1571, 1619, 1667, 1787, 1811, 1907, 1931, 1979, 2003, 2027, 2099, 2243, 2267 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant=-96.

Except for 3, also primes of the forms 8*x^2+8*x*y+11*y^2 and 11*x^2+6*x*y+27*y^2. See A140633. - T. D. Noe, May 19 2008

Except for the first member, 3, all the members seem to be terms of A123239 which are prime in both k(i) and k(rho). - A.K. Devaraj, Nov 24 2009

Conjecture: If k=2*m+1 is prime where m is an odd number with the property that 3^m mod n == 1 and m^m mod n == 1, then k belongs to this sequence. - Alzhekeyev Ascar M, May 27 2016

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

Except for 3, the terms are congruent to 11 (mod 24). - T. D. Noe, May 02 2008

MATHEMATICA

QuadPrimes2[3, 0, 8, 10000] (* see A106856 *)

PROG

(MAGMA) [3] cat[ p: p in PrimesUpTo(3000) | p mod 24 in {11} ]; // Vincenzo Librandi, Jul 23 2012

CROSSREFS

Cf. A139827.

Sequence in context: A308487 A164291 A137690 * A199854 A242384 A225809

Adjacent sequences:  A107004 A107005 A107006 * A107008 A107009 A107010

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 09 2005

STATUS

approved

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Last modified May 16 12:25 EDT 2021. Contains 343947 sequences. (Running on oeis4.)