A260553 Primes p such that p = q^2 + 2*r^2 where q and r are also primes.

17, 43, 59, 67, 107, 139, 251, 307, 347, 379, 547, 587, 859, 1699, 1867, 1931, 3371, 3499, 3739, 4507, 5059, 5347, 6907, 6971, 7451, 10091, 10627, 10667, 11467, 12491, 18787, 20411, 21227, 22907, 29947, 32059, 32779, 37547, 38651, 39619, 49307, 49747, 53147

Offset

1,1

Links

Colin Barker and Chai Wah Wu, Table of n, a(n) for n = 1..1873 n = 1..150 from Colin Barker.

Example

43 is in the sequence because 43 = 5^2 + 2*3^2 and 43, 5 and 3 are all primes.

Mathematica

Select[#1^2 + 2 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 60, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *)

Prog

(PARI) lista(nn)=forprime(p=2, nn, forprime(r=2, sqrtint(p\2), if (issquare(q2 = p-2*r^2) && isprime(sqrtint(q2)), print1(p, ", ")); ); ); \\ Michel Marcus, Jul 29 2015
(Python)
from sympy import prime, isprime
n = 5000
A260553_list, plimit = [], prime(n)**2+8
for i in range(1, n):
....q = 2*prime(i)**2
....for j in range(1, n):
........p = q + prime(j)**2
........if p < plimit and isprime(p):
............A260553_list.append(p)
A260553_list = sorted(A260553_list) # Chai Wah Wu, Jul 30 2015

Crossrefs

Main entry for this sequence is A201613.

Cf. A260554, A260555, A260556, A260557.

Sequence in context: A118587 A215164 A123592 * A165285 A200321 A165981

Adjacent sequences: A260550 A260551 A260552 * A260554 A260555 A260556

Keyword

nonn

Author

Colin Barker, Jul 29 2015

Status

approved