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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A040007 Continued fraction for sqrt(11). 3
3, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Eventual period is (3,6). - Zak Seidov, Mar 05 2011

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0, 1).

FORMULA

a(n) = (1/2)(9 + 3*(-1)^n) - 3*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 11 2009

EXAMPLE

3.316624790355399849114932736... = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009

MAPLE

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

MATHEMATICA

ContinuedFraction[Sqrt[11], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(11)); for (n=0, 20000, write("b040007.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A010468 Decimal expansion. - Harry J. Smith, Jun 02 2009

Sequence in context: A020813 A034188 A184849 * A110634 A324467 A151787

Adjacent sequences:  A040004 A040005 A040006 * A040008 A040009 A040010

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

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 November 18 10:08 EST 2019. Contains 329261 sequences. (Running on oeis4.)