A040019 Continued fraction for sqrt(24).

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

Offset

0,1

Comments

Decimal expansion of 23/55. - R. J. Mathar, Aug 25 2025

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

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2^e) = 8, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 7/2^s). (End)

G.f.: (4 + x + 4*x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

Example

4.898979485566356196394568149... = 4 + 1/(1 + 1/(8 + 1/(1 + 1/(8 + ...)))). - Harry J. Smith, Jun 03 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[24], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 120, {8, 1}] (* Harvey P. Dale, Oct 24 2022 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(24)); for (n=0, 20000, write("b040019.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A010480 (decimal expansion), A010689.

Sequence in context: A085994 A179836 A334451 * A240776 A382600 A394997

Adjacent sequences: A040016 A040017 A040018 * A040020 A040021 A040022

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved