A207524 Number of rational numbers p/q such that 0<p<q<=n and p/q<=(greatest quotient of consecutive Fibonacci numbers having denominator <= n).

1, 3, 4, 7, 8, 12, 15, 19, 21, 28, 31, 39, 43, 48, 53, 64, 68, 80, 86, 94, 100, 115, 120, 133, 141, 153, 161, 180, 186, 206, 217, 230, 240, 256, 264, 288, 300, 316, 326, 353, 361, 389, 403, 419, 433, 464, 475, 503, 517, 538, 554, 589, 601, 627, 643, 667

Offset

2,2

Comments

Counts certain consecutive Farey fractions of order n.

Not the same as A207525, which counts p/q<=(the quotient of consecutive Fibonacci numbers which has the greatest denominator <=n).

Links

Table of n, a(n) for n=2..57.

Example

a(4)=4 counts 1/4, 1/3, 1/2, 2/3.
a(5)=7 counts 1/4, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3.

Mathematica

r[n_] := Union[Flatten[Table[p/q, {q, 2, n - 1},
 {p, 1, q - 1}]]];
t = Table[r[n], {n, 3, 8}]
f[n_] := Fibonacci[n];
g = Table[f[k]/f[k + 1], {k, 1, 100}];
s[n_] := Max[Intersection[r[n + 2], g]]
Flatten[Table[Position[r[n + 2], s[n]], {n, 1, 60}]]

Crossrefs

Cf. A207525.

Sequence in context: A182079 A129819 A025032 * A003141 A338467 A284491

Adjacent sequences: A207521 A207522 A207523 * A207525 A207526 A207527

Keyword

nonn

Author

Clark Kimberling, Feb 18 2012

Status

approved