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%I #14 Aug 31 2018 09:41:53
%S 2,12,13,24,27,34,54,84,112,133,162,234,237,279,342,399,652,834,864
%N Conjectured to be complete list of numbers not of the form 4*x^2 + 4*y^2 + triangular number.
%H Ben Kane and Zhi-Wei Sun, <a href="http://arxiv.org/abs/0808.2761">On almost universal mixed sums of squares and triangular numbers</a>, arXiv:0808.2761
%t r[k_] := Reduce[x >= 0 && y >= 0 && z >= 0 && k == 4x^2 + 4y^2 + z(z+1)/2, {x, y, z}, Integers];
%t Reap[For[k=1, k <= 1000, k++, If[r[k]===False, Print[k]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Aug 31 2018 *)
%Y Cf. A001481, A141386, A141423, A141428, A141443, A141463.
%Y Cf. A141464, A141491, A141497.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 05 2008
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