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
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Fibonacci[BitLength[Range[100]] + 1] (* Paolo Xausa, Oct 16 2024 *)
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PARI
g(n)=if(n<2,1,if(n%2,g(n-1),1/g(n/2)+1)) a(n)=numerator(g(n))
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PARI
a(n)=fibonacci(ceil(log(n+1)/log(2))+1)
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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
Extensions
Offset changed to 1 by Paolo Xausa, Oct 16 2024