login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071915 Number of 1's in continued fraction expansion of (3/2)^n. 0
0, 0, 1, 0, 2, 3, 3, 6, 3, 5, 1, 2, 8, 2, 3, 5, 2, 3, 3, 6, 10, 8, 6, 4, 2, 3, 6, 5, 2, 9, 12, 7, 17, 10, 7, 9, 8, 10, 13, 13, 10, 12, 14, 9, 11, 10, 11, 6, 9, 5, 3, 13, 13, 19, 18, 13, 8, 12, 15, 14, 18, 7, 19, 19, 17, 15, 13, 14, 16, 13, 20, 16, 10, 20, 25, 17, 19, 14, 19, 14, 18, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

It seems that lim n ->infinity a(n)/n = 0.2... << (log(4)-log(3))/log(2) = 0.415... the expected density of 1's (cf. measure theory of continued fraction).

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

The continued fraction of (3/2)^24 is [16834, 8, 1, 10, 2, 25, 1, 3, 1, 1, 57, 6] which contains 4 "1's", hence a(24)=4.

PROG

(PARI) for(n=1, 200, s=contfrac(frac((3/2)^n)); print1(sum(i=1, length(s), if(1-component(s, i), 0, 1)), ", "))

CROSSREFS

Cf. A071337, A071316, A071315, A071529.

Sequence in context: A323713 A054892 A104570 * A182578 A021432 A274824

Adjacent sequences:  A071912 A071913 A071914 * A071916 A071917 A071918

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 13 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)