A047652 Primes for which golden mean is a cubic residue.

139, 151, 199, 331, 541, 619, 661, 709, 811, 829, 919, 1069, 1231, 1279, 1291, 1381, 1471, 1579, 1699, 1999, 2161, 2221, 2239, 2251, 2281, 2371, 2389, 2521, 2659, 2689, 2749, 3001, 3121, 3271, 3331, 3391, 3499, 3529, 3571, 3631, 3919, 4021, 4051, 4159

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Primes of the form x^2 + xy + 34y^2, whose discriminant is -135. - T. D. Noe, May 17 2005

Primes of the form x^2 + 135*y^2. - Arkadiusz Wesolowski, May 31 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• E. Lehmer, On the quadratic character of the Fibonacci root, Fib. Quart., 4 (1966), 135-138.
• E. Lehmer, On the quadratic character of the Fibonacci root (annotated scanned copy)

Crossrefs

Cf. A047650.

Programs

Mathematica

Select[Prime[Range[1000]],IntegerQ[Fibonacci[(#1-1)/3]/#1]&] (* Alexander Adamchuk, Sep 16 2006 *)

Formula

Primes p that divide Fibonacci((p-1)/3). - Alexander Adamchuk, Sep 16 2006

Extensions

More terms from James Sellers, Jan 25 2000