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%I #9 Jun 08 2015 20:26:55
%S 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,
%T 36,37,38,39,40,43,44,45,47,50,55,57,59,60,61,63,65,69,70,71,73,76,81,
%U 89,91,93,95,97,99,102,105,111,112,113,115,118,123,131,144
%N Ordered sums f+2*g, where f and g are positive Fibonacci numbers (A000045).
%t c = 1; d = 2; 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 ]] (* A191838 *)
%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 ]] (* A191839: f(i)-2*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 ]] (* A191840: 2*f(i)-f(j) *)
%t v3 = Union[v1, v2] (* A191841 *)
%t With[{nn=20},Take[Union[#[[1]]+2#[[2]]&/@Tuples[Fibonacci[ Range[20]], 2]],4nn]] (* _Harvey P. Dale_, Jun 08 2015 *)
%Y Cf. A191839, A191840, A191841.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jun 17 2011
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