A010125 Continued fraction for sqrt(21).

4, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1

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 (0,0,0,0,0,1).

Formula

a(n) = gcd(Fibonacci(n), Fibonacci(n-6)), n > 0. - Gary Detlefs, Dec 29 2010

Example

4.582575694955840006588047193... = 4 + 1/(1 + 1/(1 + 1/(2 + 1/(1 + ...)))). - Harry J. Smith, Jun 03 2009

Mathematica

ContinuedFraction[Sqrt[21], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 120, {8, 1, 1, 2, 1, 1}] (* Harvey P. Dale, May 16 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(21)); for (n=0, 20000, write("b010125.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A041032/A041033 (convergents), A010477 (decimal expansion).

Sequence in context: A119591 A333782 A304876 * A239114 A010324 A016525

Adjacent sequences: A010122 A010123 A010124 * A010126 A010127 A010128

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved