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A192045
Ordered sums 3f+5g, where f and g are Lucas numbers (A000032 beginning at 1).
4
8, 14, 17, 18, 23, 24, 26, 27, 29, 32, 36, 38, 41, 44, 47, 48, 53, 56, 58, 59, 64, 67, 68, 69, 74, 76, 88, 89, 92, 93, 99, 102, 107, 109, 111, 122, 123, 142, 144, 146, 148, 154, 156, 157, 161, 166, 176, 177, 178, 196, 199, 231, 232, 233, 238, 243, 244, 247
OFFSET
1,1
MATHEMATICA
c = 3; 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]] (* A192045 *)
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]] (*A 192046: 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]] (* A192047: d*f(i)-c*f(j) *)
v3 = Union[v1, v2] (* A192048 *)
Union[3First[#]+5Last[#]&/@Tuples[LucasL[Range[10]], 2]] (* Harvey P. Dale, May 04 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 21 2011
STATUS
approved