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A047650 Primes for which golden mean tau is a quadratic residue. 8
29, 89, 101, 181, 229, 349, 401, 461, 509, 521, 541, 709, 761, 769, 809, 941, 1009, 1021, 1049, 1061, 1109, 1229, 1249, 1289, 1361, 1409, 1549, 1601, 1621, 1669, 1709, 1721, 1741, 1789, 1861, 2029, 2069, 2081, 2089, 2389, 2441, 2621, 2729, 2801, 2861 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Primes of the form x^2+20y^2. - T. D. Noe, May 08 2005

Also primes p that divide the sum of cubes of the first (p-1)/2 Fibonacci numbers A005968[(p-1)/2]. - Alexander Adamchuk, Aug 07 2006

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1700

E. Lehmer, On the quadratic character of the Fibonacci root, Fib. Quart., 4 (1966), 135-138.

E. Lehmer, Correction, Fib. Quart., 4 (1966), 135-138.

E. Lehmer, On the quadratic character of the Fibonacci root (annotated scanned copy)

MATHEMATICA

nn=20; pMax=3000; Union[Reap[Do[p=x^2 + nn*y^2; If[p<=pMax&&PrimeQ[p], Sow[p]], {x, Sqrt[pMax]}, {y, Sqrt[pMax/nn]}]][[2, 1]]] (* Vincenzo Librandi, Sep 05 2016 *)

PROG

(MAGMA) k:=20; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Vincenzo Librandi, Sep 05 2016

CROSSREFS

Cf. A047651, A001583.

Cf. A005968.

Sequence in context: A042656 A042658 A042660 * A141883 A142791 A325073

Adjacent sequences:  A047647 A047648 A047649 * A047651 A047652 A047653

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Jan 25 2000

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)