A256798 Numbers whose minimal alternating squares representation has trace 2 or -2.

2, 7, 14, 18, 23, 29, 34, 42, 47, 50, 57, 62, 67, 74, 79, 82, 86, 93, 98, 103, 107, 114, 119, 126, 130, 137, 142, 146, 151, 155, 162, 167, 173, 178, 182, 189, 194, 202, 207, 211, 218, 223, 227, 233, 238, 242, 249, 254, 260, 266, 271, 275, 282, 287, 290, 295

Offset: 1

Author

Clark Kimberling, Apr 13 2015

Keywords

• nonn
• easy

Comments

The trace of all other positive integers is h^2 or -h^2 for some integer h. (See A256789 for definitions and A256791 for traces.)

Examples

			Trace(n) = 2 for n = 7, 14, 23, 34, 47, 62, ..
Trace(n) = -2 for n = 2, 18, 29, 42, 50, 57, 67, ...
Together in increasing order:  2, 7, 14, 18, 23, 29, 34, 42, ...
		

Crossrefs

Cf. A256789, A256791.

Programs

Mathematica

b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, 2 n - 1}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[r[n], {n, 0, 120}]  (* A256789 *)
u = Flatten[Table[Last[r[n]], {n, 1, 1000}]]; (* A256791 *)
Select[Range[800], Abs[u[[#]]] == 2 &] (* A256798 *)