A033199 Primes of form x^2+6*y^2.
7, 31, 73, 79, 97, 103, 127, 151, 193, 199, 223, 241, 271, 313, 337, 367, 409, 433, 439, 457, 463, 487, 577, 601, 607, 631, 673, 727, 751, 769, 823, 919, 937, 967, 991, 1009, 1033, 1039, 1063, 1087, 1129, 1153, 1201, 1231, 1249, 1279, 1297, 1303, 1321, 1327, 1399, 1423, 1447, 1471, 1489, 1543
Offset: 1
Links
- N. J. A. Sloane and Vincenzo Librandi, Table of n, a(n) for n = 1..10000 (The first 2000 terms were found by Vincenzo Librandi)
- David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989, p. 36.
- N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
Programs
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Magma
[p: p in PrimesUpTo(1600) | NormEquation(6,p) eq true]; // Bruno Berselli, Jul 03 2016
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Mathematica
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 *) -
PARI
select(n->n%24==1||n%24==7, primes(100)) \\ Charles R Greathouse IV, Nov 09 2012
Formula
Same as primes congruent to 1 or 7 mod 24. See e.g. Cox, p. 36.
a(n) ~ 4n log n. - Charles R Greathouse IV, Nov 09 2012
Extensions
Removed defective Mma program; extended the b-file using Charles R Greathouse's PARI program. - N. J. A. Sloane, Jun 06 2014
Comments