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%I #22 Mar 17 2023 09:55:34
%S 0,2,12,46,120,122,828,6554,28560,86158,145668,246046,3369960,
%T 17021162,58317492,128629846,13651680,1590277918,9719139348,
%U 37641223154,99498527400,107655263398,647549275812,5284814079046,23290743888720,71041880304722,123471611274972,182714776311554,2701419604443960,13833225534613558,47880898349909868
%N Even numbers x such that x^2 + y^2 = 13^n with x and y coprime.
%C The y values are in A188983.
%C This is also the absolute value of the imaginary part of (3+2i)^n, where i = sqrt(-1).
%H Vincenzo Librandi, <a href="/A188982/b188982.txt">Table of n, a(n) for n = 0..183</a>
%t Table[s = Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &, 1][[1]]; Select[s, EvenQ][[1]], {n, 0, 30}]
%o (Magma) [Integers()!Abs(Im((3+2*Sqrt(-1))^n)): n in [0..30]]; // _Bruno Berselli_, May 26 2011
%Y Cf. A158936, A188983.
%K nonn
%O 0,2
%A _T. D. Noe_, Apr 14 2011