A124229 Numerator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).

1, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21

Offset: 1

Author

Benoit Cloitre, Oct 20 2006

Keywords

• frac
• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A020650, A070939, A124230.

Programs

Mathematica

Fibonacci[BitLength[Range[100]] + 1] (* Paolo Xausa, Oct 16 2024 *)

PARI

g(n)=if(n<2,1,if(n%2,g(n-1),1/g(n/2)+1))
a(n)=numerator(g(n))

PARI

a(n)=fibonacci(ceil(log(n+1)/log(2))+1)

PARI

a(n)=if(n<2,1,a(n\2)+a(n\4))

Formula

a(n) = A000045(ceiling(log(n+1)/log(2))+1).

a(1)=1 then a(n) = a(floor(n/2)) + a(floor(n/4)). - Benoit Cloitre, Feb 03 2014

a(n) = A000045(A070939(n) + 1). - Paolo Xausa, Oct 17 2024

Extensions

Offset changed to 1 by Paolo Xausa, Oct 16 2024