A040021 Continued fraction for sqrt(27).

5, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5

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

a(n) = 5*(3+(-1)^n)/2 for n >= 1 with a(0) = 5. - Wesley Ivan Hurt, Feb 15 2026

Example

5.1961524227066318805823390... = 5 + 1/(5 + 1/(10 + 1/(5 + 1/(10 + ...)))). - Harry J. Smith, Jun 04 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[27], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5}, 120, {10, 5}] (* Harvey P. Dale, Jul 19 2015 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(27)); for (n=0, 20000, write("b040021.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009
(Magma) ContinuedFraction(Sqrt(27)); // G. C. Greubel, Feb 16 2018

Crossrefs

Cf. A010482 (Decimal expansion), A010721.

Sequence in context: A245088 A078560 A331064 * A339720 A341831 A360996

Adjacent sequences: A040018 A040019 A040020 * A040022 A040023 A040024

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved