A040030 Continued fraction for sqrt(37).

6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

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 (1).

Formula

From Elmo R. Oliveira, Feb 06 2024: (Start)

a(n) = 12 for n >= 1.

G.f.: 6*(1+x)/(1-x).

E.g.f.: 12*exp(x) - 6.

a(n) = 6*A040000(n) = 3*A040002(n) = 2*A040006(n). (End)

Example

6.08276253029821968899968... = 6 + 1/(12 + 1/(12 + 1/(12 + 1/(12 + ...)))). - Harry J. Smith, Jun 04 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[37], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{6}, 120, {12}] (* Harvey P. Dale, Jan 02 2017 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 44000); x=contfrac(sqrt(37)); for (n=0, 20000, write("b040030.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A010491 (decimal expansion), A041060/A041061 (convergents), A248263 (Egyptian fraction).

Cf. A040000, A040002, A040006.

Sequence in context: A060479 A028998 A285057 * A315567 A315568 A315569

Adjacent sequences: A040027 A040028 A040029 * A040031 A040032 A040033

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved