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A040006 Continued fraction for sqrt(10). 7
3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

The convergents are given in A005667(n+1)/A005668(n+1), n >= 0. - Wolfdieter Lang, Nov 23 2017

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 (1).

FORMULA

a(n) = 6 - 3*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 11 2009

a(n) = 3 + 3*sign(n). a(n) = 6, n > 0. - Wesley Ivan Hurt, Nov 01 2013

EXAMPLE

3.162277660168379331998893544... = 3 + 1/(6 + 1/(6 + 1/(6 + 1/(6 + ...)))).

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[10], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)

PROG

(PARI) allocatemem(932245000); default(realprecision, 33000); x=contfrac(sqrt(10)); for (n=0, 20000, write("b040006.txt", n, " ", x[n+1])); \\ Harry J. Smith, Jun 02 2009

(MAGMA) [6-3*(Binomial(2*n, n) mod 2): n in [0..100]]; // Vincenzo Librandi, Jan 03 2016

CROSSREFS

Cf. A010467 (decimal expansion), A005667(n+1)/A005668(n+1).

Sequence in context: A187601 A113737 A292165 * A155067 A094011 A295558

Adjacent sequences:  A040003 A040004 A040005 * A040007 A040008 A040009

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 22 06:17 EST 2018. Contains 299430 sequences. (Running on oeis4.)