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A040008 Continued fraction for sqrt(12). 3
3, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Eventual period is (2,6). - 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) = 4 + 2*(-1)^n - 3*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 11 2009

EXAMPLE

3.464101615137754587054892683... = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[12], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(12)); for (n=0, 20000, write("b040008.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A010469 Decimal expansion. - Harry J. Smith, Jun 02 2009

Sequence in context: A061187 A248082 A021758 * A129354 A129628 A245691

Adjacent sequences:  A040005 A040006 A040007 * A040009 A040010 A040011

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 15 14:06 EST 2019. Contains 329149 sequences. (Running on oeis4.)