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A124229
Numerator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).
2
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
1,2
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
MATHEMATICA
Fibonacci[BitLength[Range[100]] + 1] (* Paolo Xausa, Oct 16 2024 *)
PROG
(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))
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Benoit Cloitre, Oct 20 2006
EXTENSIONS
Offset changed to 1 by Paolo Xausa, Oct 16 2024
STATUS
approved