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%I #10 Mar 01 2023 04:47:07
%S 1,3,4,7,8,12,15,19,21,28,31,39,43,48,53,64,68,80,86,94,100,115,120,
%T 133,141,153,161,180,186,206,217,230,240,256,264,288,300,316,326,353,
%U 361,389,403,419,433,464,475,503,517,538,554,589,601,627,643,667
%N Number of rational numbers p/q such that 0<p<q<=n and p/q<=(greatest quotient of consecutive Fibonacci numbers having denominator <= n).
%C Counts certain consecutive Farey fractions of order n.
%C Not the same as A207525, which counts p/q<=(the quotient of consecutive Fibonacci numbers which has the greatest denominator <=n).
%e a(4)=4 counts 1/4, 1/3, 1/2, 2/3.
%e a(5)=7 counts 1/4, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3.
%t r[n_] := Union[Flatten[Table[p/q, {q, 2, n - 1},
%t {p, 1, q - 1}]]];
%t t = Table[r[n], {n, 3, 8}]
%t f[n_] := Fibonacci[n];
%t g = Table[f[k]/f[k + 1], {k, 1, 100}];
%t s[n_] := Max[Intersection[r[n + 2], g]]
%t Flatten[Table[Position[r[n + 2], s[n]], {n, 1, 60}]]
%Y Cf. A207525.
%K nonn
%O 2,2
%A _Clark Kimberling_, Feb 18 2012