A191838 Ordered sums f+2*g, where f and g are positive Fibonacci numbers (A000045).

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 23, 24, 25, 27, 28, 29, 31, 34, 36, 37, 38, 39, 40, 43, 44, 45, 47, 50, 55, 57, 59, 60, 61, 63, 65, 69, 70, 71, 73, 76, 81, 89, 91, 93, 95, 97, 99, 102, 105, 111, 112, 113, 115, 118, 123, 131, 144

Offset: 1

Author

Clark Kimberling, Jun 17 2011

Keywords

• nonn

Crossrefs

Cf. A191839, A191840, A191841.

Programs

Mathematica

c = 1; d = 2; f[n_] := Fibonacci[n];
g[n_] := c*f[n]; h[n_] := d*f[n];
t[i_, j_] := h[i] + g[j];
u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
v = Union[Flatten[u ]]    (* A191838 *)
t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
v1 = Union[Flatten[u1 ]]  (* A191839: f(i)-2*f(j) *)
g1[n_] := d*f[n]; h1[n_] := c*f[n];
t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
v2 = Union[Flatten[u2 ]]  (* A191840: 2*f(i)-f(j) *)
v3 = Union[v1, v2]        (* A191841 *)
With[{nn=20},Take[Union[#[[1]]+2#[[2]]&/@Tuples[Fibonacci[ Range[20]], 2]],4nn]] (* Harvey P. Dale, Jun 08 2015 *)