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

%I A260556 #18 May 22 2025 10:21:43
%S A260556 41,97,193,241,401,433,601,977,1033,1361,1753,2281,2897,3793,4241,
%T A260556 4561,5113,6737,6961,7993,10273,11953,12841,13457,17681,22273,22481,
%U A260556 26641,27961,32833,37321,42641,49801,49937,54361,57193,58153,63073,63377,76801,94321
%N A260556 Primes p such that p = q^2 + 8*r^2 where q and r are also primes.
%H A260556 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 A260556 601 is in the sequence because 601 = 23^2 + 8*3^2 and 601, 23 and 3 are all primes.
%t A260556 Select[#1^2 + 8 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 80, 2], PrimeQ] // Sort (* _Michael De Vlieger_, Jul 29 2015 *)
%o A260556 (Python)
%o A260556 from sympy import prime, isprime
%o A260556 n = 5000
%o A260556 A260556_list, plimit = [], prime(n)**2+32
%o A260556 for i in range(1,n):
%o A260556     q = 8*prime(i)**2
%o A260556     for j in range(1,n):
%o A260556         p = q + prime(j)**2
%o A260556         if p < plimit and isprime(p):
%o A260556             A260556_list.append(p)
%o A260556 A260556_list = sorted(A260556_list) # _Chai Wah Wu_, Jul 30 2015
%o A260556 (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 A260556 Cf. A260553, A260554, A260555, A260557.
%K A260556 nonn
%O A260556 1,1
%A A260556 _Colin Barker_, Jul 29 2015