A141273 Conjectured to be complete list of numbers not of the form 4*x^2 + 4*y^2 + triangular number.

2, 12, 13, 24, 27, 34, 54, 84, 112, 133, 162, 234, 237, 279, 342, 399, 652, 834, 864

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Ben Kane and Zhi-Wei Sun, On almost universal mixed sums of squares and triangular numbers, arXiv:0808.2761

Mathematica

r[k_] := Reduce[x >= 0 && y >= 0 && z >= 0 && k == 4x^2 + 4y^2 + z(z+1)/2, {x, y, z}, Integers];
Reap[For[k=1, k <= 1000, k++, If[r[k]===False, Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Aug 31 2018 *)

Crossrefs

Cf. A001481, A141386, A141423, A141428, A141443, A141463.

Cf. A141464, A141491, A141497.

Sequence in context: A032931 A072483 A081539 * A010097 A103761 A286241

Adjacent sequences: A141270 A141271 A141272 * A141274 A141275 A141276

Keyword

nonn

Author

N. J. A. Sloane, Sep 05 2008

Status

approved