A191891 - OEIS

%I #12 Apr 06 2017 17:28:42

%S 9,13,14,17,18,19,22,23,25,27,29,30,33,35,37,42,44,45,47,48,52,57,60,

%T 62,67,69,72,73,77,85,89,92,94,97,99,109,113,117,124,125,137,141,146,

%U 149,151,157,161,174,176,178,182,189,190,201,202,222,225,230,235

%N Ordered sums 4*f+5*g, where f and g are positive Fibonacci numbers (A000045).

%H Robert Israel, <a href="/A191891/b191891.txt">Table of n, a(n) for n = 1..10000</a>

%p F:= [seq(combinat:-fibonacci(n),n=2..20)]:

%p N:= 4*F[-1]+5:

%p sort(select(`<=`,convert({seq(seq(4*f+5*g,g=F),f=F)},list),N)); # _Robert Israel_, Apr 06 2017

%t c = 4; d = 5; f[n_] := Fibonacci[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 ]]    (* A191891 *)

%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 ]]  (* A191892: 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 ]]  (* A191893: d*f(i)-c*f(j) *)

%t v3 = Union[v1, v2]        (* A191894*)

%Y Cf. A191892, A191893, A191894, A191876, A191883, A191887.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jun 18 2011

%E Name improved by _Robert Israel_, Apr 06 2017