A010156 Continued fraction for sqrt(78).

8, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 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) = 4, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 3/2^s + 4/4^(s-1)). (End)

Example

8.83176086632784685476404272... = 8 + 1/(1 + 1/(4 + 1/(1 + 1/(16 + ...)))). - Harry J. Smith, Jun 09 2009

Mathematica

ContinuedFraction[Sqrt[78], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
PadRight[{8}, 120, {16, 1, 4, 1}] (* Harvey P. Dale, Sep 10 2023 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(78)); for (n=0, 20000, write("b010156.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

Crossrefs

Cf. A010530 (decimal expansion).

Sequence in context: A110194 A199283 A079359 * A197590 A154190 A019981

Adjacent sequences: A010153 A010154 A010155 * A010157 A010158 A010159

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved