A010153 Continued fraction for sqrt(75) (or 5*sqrt(3)).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Examples

			8.66025403784438646763723170... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 02 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 (0,0,0,1).

Crossrefs

Cf. A010527.

Programs

Mathematica

ContinuedFraction[Sqrt[75],300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
PadRight[{8},120,{16,1,1,1}] (* Harvey P. Dale, Oct 05 2024 *)

PARI

{ allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(75)); for (n=0, 20000, write("b010153.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

Formula

From Amiram Eldar, Nov 13 2023: (Start)

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

Dirichlet g.f.: zeta(s) * (1 + 15/4^s). (End)