A040012 Continued fraction for sqrt(17).

4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset

0,1

Comments

Decimal expansion of 22/45. - Elmo R. Oliveira, Feb 06 2024

References

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

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §4.4 Powers and Roots, p. 144.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Pages 275-276.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac.

Index entries for continued fractions for constants.

Index to divisibility sequences.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = 4*A040000(n). - Stefano Spezia, May 14 2023

From Elmo R. Oliveira, Feb 06 2024: (Start)

a(n) = 8 for n >= 1.

G.f.: 4*(1+x)/(1-x).

E.g.f.: 8*exp(x) - 4. (End)

Example

4.123105625617660549821409855... = 4 + 1/(8 + 1/(8 + 1/(8 + 1/(8 + ...)))). - Harry J. Smith, Jun 03 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[17], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 100, 8] (* Harvey P. Dale, Jun 22 2015 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 37000); x=contfrac(sqrt(17)); for (n=0, 20000, write("b040012.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A041024/A041025 (convergents), A010473 (decimal expansion), A248245 (Egyptian fraction).

Cf. A040000.

Sequence in context: A200357 A201405 A331067 * A054006 A394511 A029679

Adjacent sequences: A040009 A040010 A040011 * A040013 A040014 A040015

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved