login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109168 Continued fraction expansion of constant x (A109169) such that the continued fraction of 2*x yields the continued fraction of x interleaved with positive even numbers. 7
1, 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, 9, 10, 10, 12, 11, 12, 12, 16, 13, 14, 14, 16, 15, 16, 16, 32, 17, 18, 18, 20, 19, 20, 20, 24, 21, 22, 22, 24, 23, 24, 24, 32, 25, 26, 26, 28, 27, 28, 28, 32, 29, 30, 30, 32, 31, 32, 32, 64, 33, 34, 34, 36, 35, 36, 36, 40, 37, 38, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Compare with continued fraction A100338.

LINKS

Table of n, a(n) for n=1..75.

FORMULA

For n>=1: a(2*n-1) = n, a(2*n) = 2*a(n).

a((2*n-1)*2^p) = n * 2^p, p>=0. [Johannes W. Meijer, Jun 22 2011]

a(n) = n - (n AND n-1)/2. - Gary Detlefs, Jul 10 2014

a(n) = A285326(n)/2. - Antti Karttunen, Apr 19 2017

EXAMPLE

x=1.408494279228906985748474279080697991613998955782051281466263817524862977...

The continued fraction expansion of 2*x = A109170:

[2;1, 4,2, 6,2, 8,4, 10,3, 12,4, 14,4, 16,8, 18,5, ...]

which equals the continued fraction of x interleaved with even numbers.

MAPLE

nmax:=75; pmax:= ceil(log(nmax)/log(2)); for p from 0 to pmax do for n from 1 to nmax do a((2*n-1)*2^p):= n*2^p: od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jun 22 2011

PROG

(PARI) a(n)=if(n%2==1, (n+1)/2, 2*a(n/2))

(Scheme, with memoization-macro definec)

(definec (A109168 n) (if (zero? n) n (if (odd? n) (/ (+ 1 n) 2) (* 2 (A109168 (/ n 2))))))

;; Antti Karttunen, Apr 19 2017

CROSSREFS

Cf. A109169 (digits of x), A109170 (continued fraction of 2*x), A109171 (digits of 2*x).

Cf. A006519 and A129760. [Johannes W. Meijer, Jun 22 2011]

Half the terms of A285326.

Sequence in context: A086835 A046701 A140472 * A015134 A171580 A246796

Adjacent sequences:  A109165 A109166 A109167 * A109169 A109170 A109171

KEYWORD

cofr,nonn

AUTHOR

Paul D. Hanna, Jun 21 2005

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 May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)