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A010123 Continued fraction for sqrt(14). 5
3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 56. [From Olivier Gérard, May 22 2009]

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, 0, 0, 1).

FORMULA

a(n) = (1/6)*(-5*(n mod 4) + 4*((n+1) mod 4) + ((n+2) mod 4) + 10*((n+3) mod 4)) - 3*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jun 11 2009

a(n) = 1 + floor((n+2)/4) - floor((n+1)/4) + 5*(floor((n+4)/4) - floor((n+3)/4)) for n > 0. - Wesley Ivan Hurt, Apr 10 2017

EXAMPLE

3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009

MATHEMATICA

ContinuedFraction[Sqrt[14], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PadRight[{3}, 120, {6, 1, 2, 1}] (* Harvey P. Dale, Jan 16 2017 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A010471 Decimal expansion. - Harry J. Smith, Jun 02 2009

Sequence in context: A135261 A102774 A131918 * A039620 A008296 A140185

Adjacent sequences:  A010120 A010121 A010122 * A010124 A010125 A010126

KEYWORD

nonn,cofr

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)