A040056 Continued fraction for sqrt(65).

8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 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 to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

From Elmo R. Oliveira, Feb 10 2024: (Start)

a(n) = 16 for n >= 1.

G.f.: 8*(1+x)/(1-x).

E.g.f.: 16*exp(x) - 8.

a(n) = 8*A040000(n) = 4*A040002(n) = 2*A040012(n). (End)

Example

8.06225774829854965236661... = 8 + 1/(16 + 1/(16 + 1/(16 + 1/(16 + ...)))).

Maple

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

Mathematica

ContinuedFraction[Sqrt[65], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
PadRight[{8}, 120, {16}] (* Harvey P. Dale, Nov 27 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 49000); x=contfrac(sqrt(65)); for (n=0, 20000, write("b040056.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

Crossrefs

Cf. A010517 (decimal expansion), A041112/A041113 (convergents), A248289 (Egyptian fraction).

Cf. A040000, A040002, A040012.

Sequence in context: A217178 A103699 A238835 * A242890 A224550 A204651

Adjacent sequences: A040053 A040054 A040055 * A040057 A040058 A040059

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved