A192049 Ordered sums 4*f+5*g, where f and g are Lucas numbers (A000032 beginning at 1).

9, 17, 19, 21, 24, 27, 31, 32, 33, 36, 39, 43, 47, 48, 49, 51, 59, 63, 64, 67, 71, 77, 79, 83, 87, 92, 94, 99, 102, 106, 107, 118, 121, 127, 131, 134, 136, 149, 151, 157, 161, 162, 171, 173, 189, 193, 203, 206, 208, 217, 223, 239, 243, 247, 251, 261, 263

Offset: 1

Author

Clark Kimberling, Jun 21 2011

Keywords

• nonn

Crossrefs

Cf. A192050, A192051, A192052.

Programs

Mathematica

c = 4; d = 5; 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]]    (* A192049 *)
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]]  (* A192050: 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]]  (* A192051: d*f(i)-c*f(j) *)
v3 = Union[v1, v2]       (* A192052 *)