

A020909


Number of bits in the base2 representation of the nth Fibonacci number.


4



1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 47, 48, 49, 49, 50, 51
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..74.


FORMULA

a(n) = 1 + floor( log_2( A000045(n) ) ).
a(n) = A070939(A000045(n)).  R. J. Mathar, Aug 11 2012


MATHEMATICA

f[n_] := 1 + Floor@ Log2@ Fibonacci@ n; Array[f, 74] (* Robert G. Wilson v, Jun 24 2011 *)
IntegerLength[#, 2]&/@Fibonacci[Range[80]] (* Harvey P. Dale, Feb 11 2015 *)


PROG

(PARI) a(n)={
if(n<99, return(#binary(fibonacci(n))));
localbitprec(logint(n*6351109\9148265, 2)+64);
my(s=sqrt(5), phi=(s+1)/2, x=n*log(phi)log(s));
ceil(x/log(2));
} \\ Charles R Greathouse IV, Aug 24 2021


CROSSREFS

Cf. A000045, A070939.
Sequence in context: A004523 A038372 A121930 * A075357 A094331 A135672
Adjacent sequences: A020906 A020907 A020908 * A020910 A020911 A020912


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling


EXTENSIONS

More terms from James A. Sellers


STATUS

approved



