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A191980
Ordered sums f+5g, where f and g are Lucas numbers (A000032 beginning at 1).
4
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
1,1
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 20 2011
STATUS
approved