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A040006 Continued fraction for sqrt(10). 10
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) contfrac(sqrt(10)) \\ For illustration.

(PARI) A040006(n)=if(n, 6, 3) \\ M. F. Hasler, Nov 02 2019

(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) (convergents).

Sequence in context: A292165 A327576 A331058 * 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 October 26 21:08 EDT 2020. Contains 338027 sequences. (Running on oeis4.)