A024829 a(n) = least m such that if r and s in {F(2*h-1)/F(2*h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k, where F = A000045 (Fibonacci numbers).

4, 11, 29, 173, 1063, 7074, 47753, 325961, 2228269, 15262701, 104577551, 716721983, 4912208209

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• more

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 07 2012

Crossrefs

Cf. A001000, A024830.

Programs

Mathematica

leastSeparator[seq_] := Module[{n = 1},
Table[While[Or @@ (Ceiling[n #1[[1]]] <
2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
t = Table[N[Fibonacci[2 h - 1]/Fibonacci[2 h]], {h, 1, 10}]
t1 = leastSeparator[t]
(* Peter J. C. Moses, Aug 01 2012 *)

Extensions

Corrected by Clark Kimberling, Aug 07 2012

a(11)-a(14) from Sean A. Irvine, Jul 25 2019