A260556 Primes p such that p = q^2 + 8*r^2 where q and r are also primes.

41, 97, 193, 241, 401, 433, 601, 977, 1033, 1361, 1753, 2281, 2897, 3793, 4241, 4561, 5113, 6737, 6961, 7993, 10273, 11953, 12841, 13457, 17681, 22273, 22481, 26641, 27961, 32833, 37321, 42641, 49801, 49937, 54361, 57193, 58153, 63073, 63377, 76801, 94321

Offset: 1

Author

Colin Barker, Jul 29 2015

Keywords

• nonn

Examples

			601 is in the sequence because 601 = 23^2 + 8*3^2 and 601, 23 and 3 are all primes.
		

Links

• Colin Barker and Chai Wah Wu, Table of n, a(n) for n = 1..1510 (terms for n = 1..100 from Colin Barker).

Crossrefs

Cf. A260553, A260554, A260555, A260557.

Programs

Mathematica

Select[#1^2 + 8 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 80, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *)

PARI

lista(nn) = {forprime(p=2, nn, forprime(r=2, sqrtint(p\8), if (issquare(q2 = p-8*r^2) && isprime(sqrtint(q2)), print1(p, ", "));););} \\ Michel Marcus, Aug 01 2015

Python

from sympy import prime, isprime
n = 5000
A260556_list, plimit = [], prime(n)**2+32
for i in range(1,n):
    q = 8*prime(i)**2
    for j in range(1,n):
        p = q + prime(j)**2
        if p < plimit and isprime(p):
            A260556_list.append(p)
A260556_list = sorted(A260556_list) # Chai Wah Wu, Jul 30 2015