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A040032 Continued fraction for sqrt(39). 2
6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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) = 8 + 4*(-1)^n - 6*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 09 2009

EXAMPLE

6.2449979983983982058468931... = 6 + 1/(4 + 1/(12 + 1/(4 + 1/(12 + ...)))). - Harry J. Smith, Jun 05 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[39], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

PadRight[{6}, 100, {12, 4}] (* or *) Join[{6}, LinearRecurrence[{0, 1}, {4, 12}, 100]] (* Harvey P. Dale, Feb 09 2015 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(39)); for (n=0, 20000, write("b040032.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

CROSSREFS

Cf. A010493 Decimal expansion. - Harry J. Smith, Jun 05 2009

Sequence in context: A116946 A357128 A141270 * A239394 A006582 A263586

Adjacent sequences: A040029 A040030 A040031 * A040033 A040034 A040035

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 26 18:02 EST 2023. Contains 359833 sequences. (Running on oeis4.)