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A040005

Continued fraction for sqrt(8).

2, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Decimal expansion of 106/495. - Elmo R. Oliveira, Oct 03 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) = 4, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 3/2^s). (End)

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

E.g.f.: 4*cosh(x) + sinh(x) - 2. - Elmo R. Oliveira, Oct 03 2025

EXAMPLE

2.828427124746190097603377448... = 2 + 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...)))). - Harry J. Smith, Jun 02 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[8], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(8)); for (n=0, 20000, write("b040005.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Essentially the same as A010685.

Cf. A010466 (decimal expansion), A041010/A041011 (convergents), A248238 (Egyptian fraction).

Sequence in context: A079276 A210445 A126210 * A193306 A053578 A368201

Adjacent sequences: A040002 A040003 A040004 * A040006 A040007 A040008

KEYWORD

nonn,cofr,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A040005

⇱ A040005 - OEIS