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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Examples

			8.83176086632784685476404272... = 8 + 1/(1 + 1/(4 + 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 (0,0,0,1).

Crossrefs

Cf. A010530 (decimal expansion).

Programs

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 *)

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

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)