A377229 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(F(k)*a(k)) < 1, F = Fibonacci.

2, 3, 4, 9, 44, 1486, 1357976, 1855074754595, 2975714380792664939835466, 46528348836004781630107949818181021469921360198769

Offset: 1

Author

Alois P. Heinz, Oct 20 2024

Keywords

• nonn

Examples

			s(0), s(1), ... = 0, 1/2, 5/6, 23/24, 215/216, 11879/11880, 17653679/17653680, ... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A000045, A079586, A374663, A376058, A377205, A377230.

Programs

Maple

F:= combinat[fibonacci]:
s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(F(n)*a(n))) end:
a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*F(n))) end:
seq(a(n), n=1..11);