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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A040033 Continued fraction for sqrt(40). 2
6, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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)*(15 + 9*(-1)^n) - 6*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 09 2009

EXAMPLE

6.3245553203367586639977870... = 6 + 1/(3 + 1/(12 + 1/(3 + 1/(12 + ...)))). - Harry J. Smith, Jun 05 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[40], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

LinearRecurrence[{0, 1}, {6, 3, 12}, 100] (* or *) PadRight[{6}, 100, {12, 3}] (* Harvey P. Dale, Mar 03 2018 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 32000); x=contfrac(sqrt(40)); for (n=0, 20000, write("b040033.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

CROSSREFS

Cf. A010494 Decimal expansion. - Harry J. Smith, Jun 05 2009

Sequence in context: A060534 A060445 A131894 * A165998 A322091 A050132

Adjacent sequences:  A040030 A040031 A040032 * A040034 A040035 A040036

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 July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)