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A040003 Continued fraction for sqrt(6). 4
2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 (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) = 3 + (-1)^n - 2*(binomial(2*n, n) mod 2), with n >= 0. - Paolo P. Lava, Jun 11 2009

a(n-1) = gcd(2^n, 3^n+1) (empirical). - Michel Marcus, Sep 03 2020

EXAMPLE

2.449489742783178098197284074... = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + ...)))). - Harry J. Smith, Jun 01 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[6], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(6)); for (n=0, 20000, write("b040003.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 01 2009

(MAGMA) [3+(-1)^n-2*(Binomial(2*n, n) mod 2): n in [0..100]]; // Vincenzo Librandi, Jan 03 2016

CROSSREFS

Cf. A010464 (decimal expansion).

Equals twice A040001.

Sequence in context: A054763 A100374 A045841 * A106469 A082508 A327730

Adjacent sequences:  A040000 A040001 A040002 * A040004 A040005 A040006

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 4 21:58 EST 2020. Contains 338941 sequences. (Running on oeis4.)