A124229 - OEIS

%I #27 Oct 17 2024 08:22:35

%S 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,

%T 13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,

%U 13,13,13,13,13,13,13,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21

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

%H Paolo Xausa, <a href="/A124229/b124229.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(1)=1 then a(n) = a(floor(n/2)) + a(floor(n/4)). - _Benoit Cloitre_, Feb 03 2014

%F a(n) = A000045(A070939(n) + 1). - _Paolo Xausa_, Oct 17 2024

%t Fibonacci[BitLength[Range[100]] + 1] (* _Paolo Xausa_, Oct 16 2024 *)

%o (PARI) g(n)=if(n<2,1,if(n%2,g(n-1),1/g(n/2)+1))

%o a(n)=numerator(g(n))

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

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

%Y Cf. A000045, A020650, A070939, A124230.

%K frac,nonn

%O 1,2

%A _Benoit Cloitre_, Oct 20 2006

%E Offset changed to 1 by _Paolo Xausa_, Oct 16 2024