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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Examples

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

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).

Crossrefs

Cf. A010532 (decimal expansion).

Programs

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 *)

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

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)