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A040080 Continued fraction for sqrt(90). 2
9, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2 (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) = 10 + 8*(-1)^n - 9*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 10 2009

EXAMPLE

9.4868329805051379959966806... = 9 + 1/(2 + 1/(18 + 1/(2 + 1/(18 + ...)))). - Harry J. Smith, Jun 11 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[90], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)

PadRight[{9}, 120, {18, 2}] (* Harvey P. Dale, Jun 13 2017 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 32000); x=contfrac(sqrt(90)); for (n=0, 20000, write("b040080.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

(PARI) a(n) = if (!n, 9, if (n % 2, 2, 18)); \\ Michel Marcus, Jan 03 2016

CROSSREFS

Cf. A010541 Decimal expansion. - Harry J. Smith, Jun 11 2009

Sequence in context: A248315 A256658 A094581 * A272033 A098289 A152020

Adjacent sequences:  A040077 A040078 A040079 * A040081 A040082 A040083

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)