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%I #9 May 31 2023 13:28:33
%S 2,3,7,8,12,13,15,17,18,22,23,27,28,31,32,33,37,38,39,42,43,47,48,52,
%T 53,55,57,58,60,62,63,67,68,71,72,73,77,78,79,82,83,87,88,92,93,95,97,
%U 98,102,103,107,108,111,112,113,117,118,119,122,123
%N Numbers of the form 4^i*(8j+7) or 4^i*(5j+-2).
%C The numbers not of the form x^2+5y^2+5z^2.
%H L. J. Mordell, <a href="https://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 Module[{upto=150},Select[Union[Flatten[Table[4^i {8j+7, 5j+2,5j-2},{i,0,5},{j,0,30}]]],#>0 && #<=upto&]] (* _Harvey P. Dale_, May 31 2023 *)
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jun 02 2000