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%I #15 Mar 08 2021 02:48:22
%S 3,7,11,12,15,19,23,27,28,31,35,39,43,44,47,48,51,55,59,60,63,67,71,
%T 75,76,79,83,87,91,92,95,99,103,107,108,111,112,115,119,123,124,127,
%U 131,135,139,140,143,147,151,155,156,159,163,167,171,172
%N Numbers of the form 4^i*(8*j+3) or 4^i*(8*j+7).
%C The numbers not of the form x^2+y^2+4z^2.
%C Positions of 3 in A065882. - _Clark Kimberling_, Oct 19 2016
%C The asymptotic density of this sequence is 1/3. - _Amiram Eldar_, Mar 08 2021
%H Clark Kimberling, <a href="/A055050/b055050.txt">Table of n, a(n) for n = 1..10000</a>
%H M. A. Bennett and B. Reznick, <a href="http://www.jstor.org/stable/4145011">Positive rational solutions to x^y = y^{mx}: : A Number-Theoretic Excursion</a>, Amer. Math. Monthly, 111 (No. 1, 2004), 13-21.
%H L. J. Mordell, <a href="http://dx.doi.org/10.1093/qmath/os-1.1.276">A new Waring's problem with squares of linear forms</a>, Quart. J. Math., 1 (1930), 276-288 (see p. 283).
%t t = Table[Mod[n/4^IntegerExponent[n, 4], 4], {n, 1, 160}] (*A065882*)
%t Flatten[Position[t, 3]] (*A055050*) (* _Clark Kimberling_, Oct 19 2016 *)
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jun 02 2000