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

%I A191980 #12 Jun 19 2025 20:56:05
%S A191980 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 A191980 53,56,58,59,62,64,66,67,73,81,82,84,91,93,94,96,97,101,102,108,111,
%U A191980 119,128,131,137,138,143,146,148,149,152,156,158,163,166,174
%N A191980 Ordered sums f+5g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A191980 c = 1; d = 5; f[n_] := LucasL[n];
%t A191980 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191980 t[i_, j_] := h[i] + g[j];
%t A191980 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191980 v = Union[Flatten[u]]    (* A191980 *)
%t A191980 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191980 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191980 v1 = Union[Flatten[u1]]  (* A191981: c*f(i)-d*f(j) *)
%t A191980 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191980 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191980 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191980 v2 = Union[Flatten[u2]]  (* A191982: d*f(i)-c*f(j) *)
%t A191980 v3 = Union[v1, v2]       (* A191983 *)
%t A191980 With[{nn=20},Select[Union[(#[[1]]+5#[[2]]&/@Tuples[LucasL[Range[nn]],2])],#<=LucasL[nn]+5&]] (* _Harvey P. Dale_, Dec 07 2018 *)
%Y A191980 Cf. A191981, A191982, A191983.
%K A191980 nonn
%O A191980 1,1
%A A191980 _Clark Kimberling_, Jun 20 2011