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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Examples

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

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

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).

Crossrefs

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

Cf. A040000.

Programs

Maple

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

Mathematica

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

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

Formula

From Elmo R. Oliveira, Feb 07 2024: (Start)

a(n) = 14 = A010853(n) for n >= 1.

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

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

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