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A191988 Ordered sums 2*f+5*g, where f and g are Lucas numbers beginning at 1 (A000204).

%I A191988 #13 Jun 20 2025 17:23:28
%S A191988 7,11,13,17,19,21,22,23,26,27,28,29,34,37,41,42,43,49,51,56,57,61,63,
%T A191988 69,71,73,77,78,91,92,93,96,98,99,104,109,112,113,114,126,129,147,148,
%U A191988 149,151,153,157,159,167,172,181,184,187,203,207,237,239,241,242
%N A191988 Ordered sums 2*f+5*g, where f and g are Lucas numbers beginning at 1 (A000204).
%t A191988 c = 2; d = 5; f[n_] := LucasL[n];
%t A191988 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191988 t[i_, j_] := h[i] + g[j];
%t A191988 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191988 v = Union[Flatten[u]]    (* A191988 *)
%t A191988 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191988 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191988 v1 = Union[Flatten[u1]]  (* A191989: c*f(i)-d*f(j) *)
%t A191988 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191988 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191988 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191988 v2 = Union[Flatten[u2]]  (* A191990: d*f(i)-c*f(j) *)
%t A191988 v3 = Union[v1, v2]       (* A191991 *)
%Y A191988 Cf. A000204, A191989, A191990, A191991.
%K A191988 nonn
%O A191988 1,1
%A A191988 _Clark Kimberling_, Jun 20 2011