A040003 - OEIS

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A040003

Continued fraction for sqrt(6).

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-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

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