A010126 Continued fraction for sqrt(22).

4, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2

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 (0,0,0,0,0,1).

Formula

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2^e) = 2, a(3^e) = 4, and a(p^e) = 1 for p >= 5.

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

Example

4.690415759823429554565630113... = 4 + 1/(1 + 1/(2 + 1/(4 + 1/(2 + ...)))). - Harry J. Smith, Jun 03 2009

Mathematica

ContinuedFraction[Sqrt[22], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 120, {8, 1, 2, 4, 2, 1}] (* Harvey P. Dale, Jul 02 2019 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(22)); for (n=0, 20000, write("b010126.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A041034/A041035 (convergents), A248250 (Egyptian fraction), A010478 (decimal expansion).

Sequence in context: A178141 A063987 A236269 * A021712 A307550 A309443

Adjacent sequences: A010123 A010124 A010125 * A010127 A010128 A010129

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved