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%I #9 Dec 07 2018 16:11:11
%S 6,8,9,12,16,18,19,21,22,23,24,26,27,31,33,34,36,38,39,42,44,46,49,52,
%T 53,56,58,59,62,64,66,67,73,81,82,84,91,93,94,96,97,101,102,108,111,
%U 119,128,131,137,138,143,146,148,149,152,156,158,163,166,174
%N Ordered sums f+5g, where f and g are Lucas numbers (A000032 beginning at 1).
%t c = 1; d = 5; f[n_] := LucasL[n];
%t g[n_] := c*f[n]; h[n_] := d*f[n];
%t t[i_, j_] := h[i] + g[j];
%t u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t v = Union[Flatten[u]] (* A191980 *)
%t t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t v1 = Union[Flatten[u1]] (*A 191981: c*f(i)-d*f(j) *)
%t g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t v2 = Union[Flatten[u2]] (* A191982: d*f(i)-c*f(j) *)
%t v3 = Union[v1, v2] (* A191983 *)
%t With[{nn=20},Select[Union[(#[[1]]+5#[[2]]&/@Tuples[LucasL[Range[nn]],2])],#<=LucasL[nn]+5&]] (* _Harvey P. Dale_, Dec 07 2018 *)
%Y Cf. A191981, A191981, A191982, A191983.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jun 20 2011
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