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A020909 Number of bits in the base-2 representation of the n-th 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 16:19 EDT 2022. Contains 357149 sequences. (Running on oeis4.)