A192049 - OEIS

%I #8 Jun 19 2025 20:55:51

%S 9,17,19,21,24,27,31,32,33,36,39,43,47,48,49,51,59,63,64,67,71,77,79,

%T 83,87,92,94,99,102,106,107,118,121,127,131,134,136,149,151,157,161,

%U 162,171,173,189,193,203,206,208,217,223,239,243,247,251,261,263

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

%t c = 4; d = 5; f[n_] := LucasL[n];

%t g[n_] := c*f[n]; h[n_] := d*f[n];

%t t[i_, j_] := h[i] + g[j];

%t u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];

%t v = Union[Flatten[u]]    (* A192049 *)

%t t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]

%t u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];

%t v1 = Union[Flatten[u1]]  (* A192050: c*f(i)-d*f(j) *)

%t g1[n_] := d*f[n]; h1[n_] := c*f[n];

%t t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]

%t u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];

%t v2 = Union[Flatten[u2]]  (* A192051: d*f(i)-c*f(j) *)

%t v3 = Union[v1, v2]       (* A192052 *)

%Y Cf. A192050, A192051, A192052.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jun 21 2011