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A192045 Ordered sums 3*f+5*g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A192045 #13 Jun 19 2025 20:55:47
%S A192045 8,14,17,18,23,24,26,27,29,32,36,38,41,44,47,48,53,56,58,59,64,67,68,
%T A192045 69,74,76,88,89,92,93,99,102,107,109,111,122,123,142,144,146,148,154,
%U A192045 156,157,161,166,176,177,178,196,199,231,232,233,238,243,244,247
%N A192045 Ordered sums 3*f+5*g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A192045 c = 3; d = 5; f[n_] := LucasL[n];
%t A192045 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A192045 t[i_, j_] := h[i] + g[j];
%t A192045 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192045 v = Union[Flatten[u]]    (* A192045 *)
%t A192045 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A192045 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192045 v1 = Union[Flatten[u1]]  (* A192046: c*f(i)-d*f(j) *)
%t A192045 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A192045 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A192045 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A192045 v2 = Union[Flatten[u2]]  (* A192047: d*f(i)-c*f(j) *)
%t A192045 v3 = Union[v1, v2]       (* A192048 *)
%t A192045 Union[3First[#]+5Last[#]&/@Tuples[LucasL[Range[10]],2]] (* _Harvey P. Dale_, May 04 2012 *)
%Y A192045 Cf. A000204, A191988, A192046, A192047, A192048.
%K A192045 nonn
%O A192045 1,1
%A A192045 _Clark Kimberling_, Jun 21 2011