A010132 Continued fraction for sqrt(34).

5, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10

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 12 2023: (Start)

Multiplicative with a(2) = 4, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 3/2^(2*s-1) + 3/2^s). (End)

Example

5.83095189484530047087415287... = 5 + 1/(1 + 1/(4 + 1/(1 + 1/(10 + ...)))). - Harry J. Smith, Jun 04 2009

Mathematica

ContinuedFraction[Sqrt[34], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(34)); for (n=0, 20000, write("b010132.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A010489 (decimal expansion).

Sequence in context: A194704 A108170 A086988 * A254247 A216606 A351789

Adjacent sequences: A010129 A010130 A010131 * A010133 A010134 A010135

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved