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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A260553, A260554, A260555, A260557.

Sequence in context: A039469 A124247 A256485 * A142658 A228573 A273363

Adjacent sequences: A260553 A260554 A260555 * A260557 A260558 A260559

Keyword

nonn

Author

Colin Barker, Jul 29 2015

Status

approved