A040650 Continued fraction for sqrt(677).

26, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52

Offset

0,1

Links

Table of n, a(n) for n=0..62.

Index entries for continued fractions for constants

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

Formula

From Elmo R. Oliveira, Feb 15 2024: (Start)

a(n) = 52 for n >= 1.

G.f.: 26*(1+x)/(1-x).

E.g.f.: 52*exp(x) - 26.

a(n) = 26*A040000(n) = 13*A040002(n) = 2*A040156(n). (End)

Example

26 + 1/(52 + 1/(52 + 1/(52 + 1/(52 + ...)))) = sqrt(677).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(677)), confrac);

Mathematica

PadRight[{26}, 100, 52] (* Paolo Xausa, Nov 01 2025 *)

Crossrefs

Cf. A042300/A042301 (convergents).

Cf. A040000, A040002, A040156.

Sequence in context: A249912 A267039 A122999 * A252994 A288162 A352346

Adjacent sequences: A040647 A040648 A040649 * A040651 A040652 A040653

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved