A256698 Numbers with positive triangular trace.

1, 3, 4, 6, 8, 10, 13, 15, 16, 19, 21, 23, 26, 28, 29, 31, 34, 36, 38, 40, 43, 45, 46, 48, 50, 53, 55, 57, 59, 61, 64, 66, 67, 69, 71, 73, 76, 78, 79, 80, 82, 84, 86, 89, 91, 93, 94, 96, 98, 100, 103, 105, 106, 108, 109, 111, 113, 115, 118, 120, 122, 124

Offset: 1

Author

Clark Kimberling, Apr 11 2015

Keywords

• nonn
• easy

Comments

Are the differences all 1, 2, or 3? See A255974 for definitions.

Examples

			R(0) = 0; trace = 0
R(1) = 1; trace = 1
R(2) = 3 - 1; trace = -1
R(3) = 3; trace = 3
R(4) = 6 - 3 + 1; trace = 1
R(5) = 6 - 1; trace = -1
R(6) = 6; trace = 6
R(7) = 10 - 3; trace = -3
Thus, 1, 3, 4, 6, ... have positive trace, and 2, 5, 7, .... have negative trace.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A255974, A256697, A256699 (complement).

Programs

Mathematica

b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, n}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
Table[Last[r[n]], {n, 0, 300}]   (* A256697 *)
Select[Range[200], Last[r[#]] > 0 &]  (* A256698 *)
Select[Range[200], Last[r[#]] < 0 &]  (* A256699 *)