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%I #13 Feb 14 2017 00:20:54
%S 41,53,313,317,337,353,373,397,457,577,1201,1213,1381,1621,2213,3461,
%T 3593,3701,3761,4481,4793,5021,5393,5801,7321,7333,7433,7541,7741,
%U 7933,8081,8161,8521,9181,9433,10133,10601,11833,12421,13933,14281,14293,14321,14341,14401,14461,14593
%N Primes p = x^2 + y^2 such that x + y is a perfect square.
%C Least prime in which either x&y is k: 577, 53, 13933, 41, 41, 397, 53, 353, 337, etc. - _Robert G. Wilson v_, Feb 13 2017
%H Charles R Greathouse IV, <a href="/A282353/b282353.txt">Table of n, a(n) for n = 1..10000</a>
%e Prime number 53 is a term because 53 = 2^2 + 7^2 and 2 + 7 = 9 is a perfect square.
%t fQ[n_] := Block[{x = 1, y, lmt = Sqrt[n/2]}, While[y = Sqrt[n - x^2]; x < lmt && (!IntegerQ@ y || !IntegerQ@ Sqrt[x + y]), x++]; x < lmt]; Select[ Prime @Range@1750, fQ] (* _Robert G. Wilson v_, Feb 13 2017 *)
%o (PARI) is(p)=p%4==1 && isprime(p) && issquare(vecsum(qfbsolve(Qfb(1, 0, 1), p))) \\ _Charles R Greathouse IV_, Feb 14 2017
%Y Cf. A002313, A282381.
%K nonn
%O 1,1
%A _Altug Alkan_, Feb 13 2017
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