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A010124 Continued fraction for sqrt(19). 2
4, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1 (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

A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).

FORMULA

a(n) = (1/90)*(-73*(n mod 6) + 2*((n+1) mod 6) + 47*((n+2) mod 6) - 13*((n+3) mod 6) + 32*((n+4) mod 6) + 107*((n+5) mod 6)) - 4*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jun 11 2009

EXAMPLE

4.358898943540673552236981983... = 4 + 1/(2 + 1/(1 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Jun 03 2009

MATHEMATICA

ContinuedFraction[Sqrt[19], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(19)); for (n=0, 20000, write("b010124.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

CROSSREFS

Cf. A010475 Decimal expansion. - Harry J. Smith, Jun 03 2009

Sequence in context: A200586 A097525 A309975 * A271310 A071406 A010311

Adjacent sequences:  A010121 A010122 A010123 * A010125 A010126 A010127

KEYWORD

nonn,cofr

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 20 17:03 EDT 2019. Contains 327242 sequences. (Running on oeis4.)