A040156 Continued fraction for sqrt(170).

13, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			13 + 1/(26 + 1/(26 + 1/(26 + 1/(26 + ...)))) = sqrt(170).
		

Links

• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A040000, A041312/A041313 (convergents).

Programs

Maple

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

Mathematica

ContinuedFraction[Sqrt[170],300] (* Vladimir Joseph Stephan Orlovsky, Mar 25 2011*)

Formula

From Elmo R. Oliveira, Feb 12 2024: (Start)

a(n) = 26 for n >= 1.

G.f.: 13*(1+x)/(1-x).

E.g.f.: 26*exp(x) - 13.

a(n) = 13*A040000(n). (End)