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A260553
Primes p such that p = q^2 + 2*r^2 where q and r are also primes.
6
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
(PARI) list(lim)=my(v=List()); lim\=1; forprime(q=2, sqrtint((lim-9)\2), my(t=2*q^2); forprime(p=3, sqrtint(lim-t), my(r=t+p^2); if(isprime(r), listput(v, r)))); Set(v) \\ Charles R Greathouse IV, Oct 09 2024
(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.
Sequence in context: A118587 A215164 A123592 * A165285 A200321 A165981
KEYWORD
nonn
AUTHOR
Colin Barker, Jul 29 2015
STATUS
approved