

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
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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



