A040011 Continued fraction for sqrt(15).

3, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6

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) = 6, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 5/2^s). (End)

Example

3.872983346207416885179265399... = 3 + 1/(1 + 1/(6 + 1/(1 + 1/(6 + ...)))). - Harry J. Smith, Jun 03 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[15], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{3}, 120, {6, 1}] (* Harvey P. Dale, Apr 14 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(15)); for (n=0, 20000, write("b040011.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A010472 (decimal expansion).

Sequence in context: A068436 A019570 A239303 * A066446 A069625 A111614

Adjacent sequences: A040008 A040009 A040010 * A040012 A040013 A040014

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved