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

Offset

0,1

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)

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

Cf. A010466 (decimal expansion). - Harry J. Smith, Jun 02 2009

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