A024830 a(n) = least m such that if r and s in {F(2*h)/F(2*h+1): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k, where F = A000045 (Fibonacci numbers).

7, 18, 73, 424, 2741, 18389, 124799, 851937, 5831634, 39952039, 273777171, 1876334786, 12860231668

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• more

Comments

See A001000 for a guide to related sequences. - Clark Kimberling, Aug 07 2012

Crossrefs

Cf. A001000, A024829.

Programs

Mathematica

(* For a guide to related sequences, see A001000. *)
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]/Fibonacci[2 h + 1]], {h, 1, 10}];
t1 = leastSeparator[t]
(* Peter J. C. Moses, Aug 01 2012 *)

Extensions

Extended by Clark Kimberling, Aug 07 2012

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