A040024 Continued fraction for sqrt(30).

5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2

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 (0,1).

Formula

G.f.: (5 + 2*x + 5*x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

Example

5.4772255750516611345696978... = 5 + 1/(2 + 1/(10 + 1/(2 + 1/(10 + ...)))). - Harry J. Smith, Jun 04 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[30], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 28000); x=contfrac(sqrt(30)); for (n=0, 20000, write("b040024.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A010485 (decimal expansion), A010700.

Sequence in context: A375613 A127098 A127097 * A196385 A178714 A036121

Adjacent sequences: A040021 A040022 A040023 * A040025 A040026 A040027

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved