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%I #33 Jun 25 2018 12:55:10
%S 2,5,13,17,29,37,41,53,73,89,137,149,157,181,257,269,281,293,313,349,
%T 373,397,401,409,421,461,541,557,577,593,661,709,733,757,769,773,797,
%U 853,937,953,1021,1049,1069,1181,1237,1277,1301,1373,1429,1433,1453,1489
%N Primes of form a^2 + b^2 such that a^4 + b^4 is prime.
%H Charles R Greathouse IV, <a href="/A182198/b182198.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 = 2^2 + 3^2, 2^4 + 3^4 = 97 is prime.
%t nn = 40; t = {}; Do[c = a^2 + b^2; If[c < nn^2 && PrimeQ[c] && PrimeQ[a^4 + b^4], AppendTo[t, c]], {a, nn}, {b, a}]; Sort[t] (* _T. D. Noe_, Apr 22 2012 *)
%t Take[#[[1]]^2+#[[2]]^2&/@Select[Tuples[Range[40],2],AllTrue[{#[[1]]^2+ #[[2]]^2, #[[1]]^4+#[[2]]^4},PrimeQ]&]//Union,60] (* _Harvey P. Dale_, Jun 25 2018 *)
%o (PARI) list(lim)=my(v=List(),t);lim\=1;for(x=1,sqrtint(lim),for(y=1, min(sqrtint(lim-x^2),x), if(isprime(t=x^2+y^2)&&isprime(x^4+y^4), listput(v,t)))); vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Apr 22 2012
%Y Subsequence of A002313.
%Y Cf. A003336 (numbers that are the sum of 2 nonzero 4th powers).
%Y Cf. A002645 (quartan primes: primes of the form x^4 + y^4).
%K nonn
%O 1,1
%A Thomas Ordowski, Apr 20 2012
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