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

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 A029679 A304651

Adjacent sequences: A040009 A040010 A040011 * A040013 A040014 A040015

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved