This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123592 #14 Aug 26 2015 12:46:19
%S A123592 17,43,59,67,83,107,139,179,227,251,307,347,379,419,467,491,547,563,
%T A123592 587,659,827,859,971,1019,1091,1259,1427,1499,1667,1699,1811,1867,
%U A123592 1907,1931,1979,2027,2243,2267,2339,2531,2579,2699,2819,2843,2939,3347,3371,3499
%N A123592 Primes of the form p^2 + q^2 + r^2, where p,q,r are primes.
%C A123592 a(n) is a subset of A085317(n) = {3, 11, 17, 19, 29, 41, 43, 53, 59, 61, 67, 73, 83, ...} Primes of form x^2 + y^2 + z^2. All terms except a(1) = 17 are congruent to 3 mod 8.
%C A123592 If neither p, q, nor r is 3, then p^2 + q^2 + r^2 is always divisible by 3. Therefore all terms in a(n) have at least one 3^2 in their summation. - _Richard R. Forberg_, Aug 29 2013
%e A123592 a(1) = 17 because 17 = 2^2 + 2^2 + 3^2 is prime and 2^2 + 2^2 + 2^2 = 12 is composite.
%t A123592 With[{nn=50},Take[Union[Select[Total/@Tuples[Prime[Range[nn/2]]^2, 3], PrimeQ]],nn]] (* _Harvey P. Dale_, Aug 26 2015 *)
%Y A123592 Cf. A085317 (primes of form x^2 + y^2 + z^2).
%K A123592 nonn
%O A123592 1,1
%A A123592 _Alexander Adamchuk_, Nov 14 2006