A040055 Continued fraction for sqrt(63).

7, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1

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 (0,1).

Formula

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2^e) = 14, and a(p^e) = 1 for p >= 5.

Dirichlet g.f.: zeta(s) * (1 + 13/2^s). (End)

Example

7.9372539331937717715048472... = 7 + 1/(1 + 1/(14 + 1/(1 + 1/(14 + ...)))). - Harry J. Smith, Jun 07 2009

Maple

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

Mathematica

ContinuedFraction[Sqrt[63], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(63)); for (n=0, 20000, write("b040055.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

Crossrefs

Cf. A010516 (decimal expansion), A020820 (decimal expansion of 1/sqrt(63)).

Sequence in context: A203810 A225017 A268919 * A317016 A348983 A013614

Adjacent sequences: A040052 A040053 A040054 * A040056 A040057 A040058

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved