A191920 Ordered sums f+3*g, where f and g are Lucas numbers (A000032 beginning at 1).

4, 6, 7, 10, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 34, 36, 37, 38, 39, 40, 41, 44, 50, 51, 55, 56, 57, 58, 59, 61, 62, 65, 68, 72, 79, 80, 83, 85, 88, 90, 91, 94, 97, 98, 101, 105, 109, 116, 126, 130, 132, 134, 135, 142, 144, 145

Offset: 1

Author

Clark Kimberling, Jun 19 2011

Keywords

• nonn

Crossrefs

Cf. A000032, A191921, A191922, A191923, A191842.

Programs

Mathematica

c = 1; d = 3; f[n_] := LucasL[n];
g[n_] := c*f[n]; h[n_] := d*f[n];
t[i_, j_] := h[i] + g[j];
u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
v = Union[Flatten[u]]    (* A191920 *)
t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
v1 = Union[Flatten[u1]]  (* A191921: c*f(i)-d*f(j) *)
g1[n_] := d*f[n]; h1[n_] := c*f[n];
t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
v2 = Union[Flatten[u2]]  (* A191922: d*f(i)-c*f(j) *)
v3 = Union[v1, v2]       (* A191923 *)