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A191924 Ordered sums 2*f+3*g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A191924 #9 Jun 19 2025 20:56:17
%S A191924 5,9,11,14,15,17,18,20,23,25,26,27,29,31,34,35,39,41,43,45,47,48,55,
%T A191924 56,57,60,61,62,67,68,69,70,76,79,89,90,91,93,95,97,101,103,106,109,
%U A191924 112,115,123,127,143,145,147,148,149,155,161,163,164,173,177,181
%N A191924 Ordered sums 2*f+3*g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A191924 c = 2; d = 3; f[n_] := LucasL[n];
%t A191924 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191924 t[i_, j_] := h[i] + g[j];
%t A191924 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191924 v = Union[Flatten[u]]    (* A191924 *)
%t A191924 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191924 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191924 v1 = Union[Flatten[u1]]  (* A191925:c*f(i)-d*f(j) *)
%t A191924 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191924 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191924 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191924 v2 = Union[Flatten[u2]]  (* A191926:d*f(i)-c*f(j) *)
%t A191924 v3 = Union[v1, v2]       (* A191927 *)
%Y A191924 Cf. A191925, A191926, A191927.
%K A191924 nonn
%O A191924 1,1
%A A191924 _Clark Kimberling_, Jun 19 2011