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

0,1

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 (0,0,0,1).

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)

Example

8.66025403784438646763723170... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(16 + ...)))). - Harry J. Smith, Jun 02 2009

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 *)

Prog

(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

Crossrefs

Cf. A010527.

Sequence in context: A276405 A066341 A181064 * A360970 A363918 A133421

Adjacent sequences: A010150 A010151 A010152 * A010154 A010155 A010156

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved