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%I #13 Mar 21 2014 14:27:15
%S 85,145,221,265,365,481,545,685,1405,1513,1985,2245,2813,2965,3281,
%T 3785,3961,4141,4705,5305,5513,5941,6161,6385,6613,7081,7813,8065,
%U 8321,9113,9385,10805,11101,11401,11705,12013,12961,13285,13945,16021,17113,17861,19405
%N Numbers k^2 + (k+1)^2 that can be expressed as a sum of two squares in exactly one other way.
%C Subsequence of A166080.
%H Giovanni Resta, <a href="/A239527/b239527.txt">Table of n, a(n) for n = 1..10000</a>
%F Each number is of the form 2y^2 + 2y + 1.
%e 365 is in the sequence because 365 = 2^2+19^2 = 13^2+14^2; in the second representation 14-13=1.
%t ok[n_] := 2 == Count[ PowersRepresentations[n, 2, 2], _?(! MemberQ[#, 0] &)]; Select[(2*#^2 + 2*# + 1) & /@ Range[100], ok] (* _Giovanni Resta_, Mar 21 2014 *)
%Y Cf. A166080, A000404, A001844.
%K nonn
%O 1,1
%A _Carmine Suriano_, Mar 21 2014