A191916 Ordered sums f+2g, where f and g are Lucas numbers (A000032 beginning at 1).

3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 29, 31, 32, 33, 35, 37, 39, 40, 43, 47, 49, 51, 53, 54, 55, 59, 61, 62, 65, 69, 76, 78, 82, 83, 84, 87, 90, 95, 97, 98, 101, 105, 112, 123, 125, 129, 131, 134, 137, 141, 145, 153, 155

Offset: 1

Author

Clark Kimberling, Jun 19 2011

Keywords

• nonn

Crossrefs

Cf. A191917, A191918, A191919, A191838.

Programs

Mathematica

c = 1; d = 2; 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 ]]    (* A191916 *)
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 ]]  (* A191917: 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 ]]  (* A191918: d*f(i)-c*f(j) *)
v3 = Union[v1, v2]         (* A191919*)