A010133 Continued fraction for sqrt(41).

6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12

Offset

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

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 (0,0,1).

Formula

From Elmo R. Oliveira, Aug 03 2024: (Start)

G.f.: 2*(3 + x + x^2 + 3*x^3)/((1 - x)*(1 + x + x^2)).

a(n) = a(n-3), n > 3. (End)

Example

6.40312423743284868648821767... = 6 + 1/(2 + 1/(2 + 1/(12 + 1/(2 + ...)))). - Harry J. Smith, Jun 05 2009

Mathematica

ContinuedFraction[Sqrt[41], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(41)); for (n=0, 20000, write("b010133.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

Crossrefs

Cf. A010495 (decimal expansion).

Cf. A041068/A041069 (convergents), A248267 (Egyptian fraction).

Sequence in context: A093497 A092138 A138995 * A065280 A247672 A188726

Adjacent sequences: A010130 A010131 A010132 * A010134 A010135 A010136

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved