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A040056 Continued fraction for sqrt(65). 6
8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 (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 to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

a(n) = 16 - 8*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 10 2009

EXAMPLE

8.06225774829854965236661... = 8 + 1/(16 + 1/(16 + 1/(16 + 1/(16 + ...))))

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[65], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 49000); x=contfrac(sqrt(65)); for (n=0, 20000, write("b040056.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

CROSSREFS

Cf. A010517 Decimal expansion.

Sequence in context: A217178 A103699 A238835 * A242890 A224550 A204651

Adjacent sequences:  A040053 A040054 A040055 * A040057 A040058 A040059

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 14 10:04 EST 2019. Contains 329111 sequences. (Running on oeis4.)