A040071 Continued fraction for sqrt(80).

8, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1

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

a(n) = 4^(1+(-1)^n) for n>0, a(0)=8. - Bruno Berselli, Dec 29 2015

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2^e) = 16, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 15/2^s). (End)

Example

8.9442719099991587856366946... = 8 + 1/(1 + 1/(16 + 1/(1 + 1/(16 + ...)))). - Harry J. Smith, Jun 09 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[80], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
PadRight[{8}, 120, {16, 1}] (* Harvey P. Dale, Apr 16 2022 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 26000); x=contfrac(sqrt(80)); for (n=0, 20000, write("b040071.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

Crossrefs

Cf. A010532 (decimal expansion).

Sequence in context: A342636 A332941 A107929 * A317026 A126000 A326992

Adjacent sequences: A040068 A040069 A040070 * A040072 A040073 A040074

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved