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%I #9 Nov 09 2015 23:06:16
%S 2,13,41,61,113,181,269,313,421,613,761,929,1013,1201,1301,1637,1741,
%T 1861,2113,2381,2521,2969,3121,3449,3613,4153,4337,4513,5101,5737,
%U 5953,6173,6389,6857,7321,7817,8069,8581,9397,9661,9941,10513,11717,12329,12641,13613,14281,14621,15313,16381,17117,17489,18253,18637,19013,19801,20201
%N Least prime of the form a^2 + b^2 with a > k and b > k, for some number k.
%C List of distinct members of A263979.
%C The sequence is infinite; see Sierpinski (1988), p. 221.
%D W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988.
%F a(n) == 1 or 2 mod 4.
%e The smallest prime of the form a^2 + b^2 with a > 2 and b > 2 is 41 = 4^2 + 5^2, so 41 is a member.
%e 5 = 1^2 + 2^2 is a prime of the form a^2 + b^2 with a > 0 and b > 0, but 5 is not a member, because 2 = 1^2 + 1^2 is a smaller prime of that form.
%t Union[Table[
%t Min[Select[
%t Union[
%t Flatten[
%t With[{n = k},
%t Array[#1^2 + #2^2 &, { 2 n + 1, 2 n + 1}, {n + 1, n + 1}]]]],
%t PrimeQ]], {k, 0, 99}]]
%Y Cf. A002144, A002313, A263979.
%K nonn
%O 1,1
%A _Jonathan Sondow_, Nov 09 2015
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