OFFSET
1,1
COMMENTS
It is a classical result that p is of the form x^2 + 5y^2 if and only if p = 5 or p == 1 or 9 mod 20 (see Cox, page 33). - N. J. A. Sloane, Sep 20 2012
Or, 5 and all primes p that divide Fibonacci((p - 1)/2) = A121568(n). - Alexander Adamchuk, Aug 07 2006
REFERENCES
David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989; see p. 33.
LINKS
Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 2000 terms from Vincenzo Librandi]
B. W. Brewer, On primes of the form u^2+5v^2, Am. Math. Monthly vol. 17 no 2 (1966) pp 502-509.
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
FORMULA
a(n) ~ 4n log n. - Charles R Greathouse IV, Nov 09 2012
MATHEMATICA
QuadPrimes2[1, 0, 5, 10000] (* see A106856 *)
PROG
(Magma) [p: p in PrimesUpTo(2000) | NormEquation(5, p) eq true]; // Bruno Berselli, Jul 03 2016
(PARI) is(n)=my(k=n%20); n==5 || ((k==9 || k==9) && isprime(n)) \\ Charles R Greathouse IV, Feb 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved