A040037 Continued fraction for sqrt(44).

6, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 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 (0,0,0,0,0,0,0,1).

Formula

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2) = 1, a(4) = 2, a(2^e) = 12 for e >= 3, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 5/2^(3*s-1) + 1/4^s). (End)

Example

6.633249580710799698229865473... = 6 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))). - Harry J. Smith, Jun 05 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[44], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{6}, 80, {12, 1, 1, 1, 2, 1, 1, 1}] (* Harvey P. Dale, Apr 02 2013 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(44)); for (n=0, 20000, write("b040037.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

Crossrefs

Cf. A010498 (decimal expansion).

Sequence in context: A293901 A324891 A260340 * A344877 A356156 A356157

Adjacent sequences: A040034 A040035 A040036 * A040038 A040039 A040040

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved