A040042 Continued fraction for sqrt(50) = 5*sqrt(2).

7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

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 07 2024: (Start)

a(n) = 14 for n >= 1.

G.f.: 7*(1+x)/(1-x).

E.g.f.: 14*exp(x) - 7.

a(n) = 7*A040000(n). (End)

Example

7.07106781186547524400844... = 7 + 1/(14 + 1/(14 + 1/(14 + 1/(14 + ...)))). - Harry J. Smith, Jun 01 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[50], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 47000); x=contfrac(sqrt(50)); for (n=0, 20000, write("b040042.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 01 2009

Crossrefs

Cf. A010503 (decimal expansion), A041084/A041085 (convergents), A248275 (Egyptian fraction).

Cf. A040000.

Sequence in context: A064666 A269160 A286418 * A233366 A232831 A232877

Adjacent sequences: A040039 A040040 A040041 * A040043 A040044 A040045

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved