A191980 Ordered sums f+5g, where f and g are Lucas numbers (A000032 beginning at 1).

6, 8, 9, 12, 16, 18, 19, 21, 22, 23, 24, 26, 27, 31, 33, 34, 36, 38, 39, 42, 44, 46, 49, 52, 53, 56, 58, 59, 62, 64, 66, 67, 73, 81, 82, 84, 91, 93, 94, 96, 97, 101, 102, 108, 111, 119, 128, 131, 137, 138, 143, 146, 148, 149, 152, 156, 158, 163, 166, 174

Offset: 1

Author

Clark Kimberling, Jun 20 2011

Keywords

• nonn

Crossrefs

Cf. A191981, A191982, A191983.

Programs

Mathematica

c = 1; 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]]    (* A191980 *)
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]]  (* A191981: 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]]  (* A191982: d*f(i)-c*f(j) *)
v3 = Union[v1, v2]       (* A191983 *)
With[{nn=20},Select[Union[(#[[1]]+5#[[2]]&/@Tuples[LucasL[Range[nn]],2])],#<=LucasL[nn]+5&]] (* Harvey P. Dale, Dec 07 2018 *)