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

0,1

Links

Table of n, a(n) for n=0..53.

Index entries for continued fractions for constants

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

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)

Example

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

Maple

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

Mathematica

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

Crossrefs

Cf. A040000, A041312/A041313 (convergents).

Sequence in context: A105796 A226051 A238338 * A296752 A297279 A095781

Adjacent sequences: A040153 A040154 A040155 * A040157 A040158 A040159

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane.

Status

approved