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Primes p such that p = q^2 + 8*r^2 where q and r are also primes.
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%I #16 Aug 02 2015 06:39:30

%S 41,97,193,241,401,433,601,977,1033,1361,1753,2281,2897,3793,4241,

%T 4561,5113,6737,6961,7993,10273,11953,12841,13457,17681,22273,22481,

%U 26641,27961,32833,37321,42641,49801,49937,54361,57193,58153,63073,63377,76801,94321

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

%H Colin Barker and Chai Wah Wu, <a href="/A260556/b260556.txt">Table of n, a(n) for n = 1..1510</a> (terms for n = 1..100 from Colin Barker).

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

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

%o (Python)

%o from sympy import prime, isprime

%o n = 5000

%o A260556_list, plimit = [], prime(n)**2+32

%o for i in range(1,n):

%o ....q = 8*prime(i)**2

%o ....for j in range(1,n):

%o ........p = q + prime(j)**2

%o ........if p < plimit and isprime(p):

%o ............A260556_list.append(p)

%o A260556_list = sorted(A260556_list) # _Chai Wah Wu_, Jul 30 2015

%o (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

%Y Cf. A260553, A260554, A260555, A260557.

%K nonn

%O 1,1

%A _Colin Barker_, Jul 29 2015