|
%I #46 Sep 08 2022 08:44:51
%S 7,31,73,79,97,103,127,151,193,199,223,241,271,313,337,367,409,433,
%T 439,457,463,487,577,601,607,631,673,727,751,769,823,919,937,967,991,
%U 1009,1033,1039,1063,1087,1129,1153,1201,1231,1249,1279,1297,1303,1321,1327,1399,1423,1447,1471,1489,1543
%N Primes of form x^2+6*y^2.
%C Appears to also be the primes p such that p mod 6 = 1 and Fibonacci(p) mod 6 = 1. - _Gary Detlefs_, May 26 2014
%H N. J. A. Sloane and Vincenzo Librandi, <a href="/A033199/b033199.txt">Table of n, a(n) for n = 1..10000</a> (The first 2000 terms were found by Vincenzo Librandi)
%H David A. Cox, <a href="http://www.math.toronto.edu/~ila/Cox-Primes_of_the_form_x2%2Bny2.pdf">Primes of the Form x^2 + n y^2</a>, Wiley, 1989, p. 36.
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%F Same as primes congruent to 1 or 7 mod 24. See e.g. Cox, p. 36.
%F a(n) ~ 4n log n. - _Charles R Greathouse IV_, Nov 09 2012
%t f[x_, y_] := x^2 + 6*y^2; lst = {}; Do[p = f[x, y]; If[ PrimeQ[ p], AppendTo[ lst, p]], {y, 20}, {x, 50}]; Take[ Union[ lst], 50] (* _Vladimir Joseph Stephan Orlovsky_, Aug 04 2009 *)
%o (PARI) select(n->n%24==1||n%24==7, primes(100)) \\ _Charles R Greathouse IV_, Nov 09 2012
%o (Magma) [p: p in PrimesUpTo(1600) | NormEquation(6,p) eq true]; // _Bruno Berselli_, Jul 03 2016
%Y Cf. A139643, primes in A002481. Cf. A107006, A107008.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_.
%E Removed defective Mma program; extended the b-file using Charles R Greathouse's PARI program. - _N. J. A. Sloane_, Jun 06 2014
|
