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Numbers of the form p^2 + q^2 + r^2 + s^2, where p, q, r, and s are primes.
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%I #5 Jul 29 2012 15:23:33

%S 16,21,26,31,36,37,42,47,52,58,61,63,66,68,71,76,79,82,84,87,92,100,

%T 103,106,108,111,116,124,127,132,133,138,143,148,151,154,156,159,164,

%U 172,175,178,180,181,183,186,188,191,196,199,202,204,207,212,220,223

%N Numbers of the form p^2 + q^2 + r^2 + s^2, where p, q, r, and s are primes.

%H T. D. Noe, <a href="/A214515/b214515.txt">Table of n, a(n) for n = 1..10000</a>

%t nn = 10^3; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ps[[i]]^2 + ps[[j]]^2 + ps[[k]]^2 + ps[[l]]^2, {i, Length[ps]}, {j, i, Length[ps]}, {k, j, Length[ps]}, {l, k, Length[ps]}]]; t = Select[t, # <= nn &]; Union[t]

%Y Cf. A045636 (two primes), A214514 (three primes).

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 29 2012