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A192049 Ordered sums 4*f+5*g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A192049 #8 Jun 19 2025 20:55:51
%S A192049 9,17,19,21,24,27,31,32,33,36,39,43,47,48,49,51,59,63,64,67,71,77,79,
%T A192049 83,87,92,94,99,102,106,107,118,121,127,131,134,136,149,151,157,161,
%U A192049 162,171,173,189,193,203,206,208,217,223,239,243,247,251,261,263
%N A192049 Ordered sums 4*f+5*g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A192049 c = 4; d = 5; f[n_] := LucasL[n];
%t A192049 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A192049 t[i_, j_] := h[i] + g[j];
%t A192049 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192049 v = Union[Flatten[u]]    (* A192049 *)
%t A192049 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A192049 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192049 v1 = Union[Flatten[u1]]  (* A192050: c*f(i)-d*f(j) *)
%t A192049 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A192049 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A192049 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192049 v2 = Union[Flatten[u2]]  (* A192051: d*f(i)-c*f(j) *)
%t A192049 v3 = Union[v1, v2]       (* A192052 *)
%Y A192049 Cf. A192050, A192051, A192052.
%K A192049 nonn
%O A192049 1,1
%A A192049 _Clark Kimberling_, Jun 21 2011