A040020 Continued fraction for sqrt(26).

5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

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).

Formula

From Elmo R. Oliveira, Feb 06 2024: (Start)

a(n) = 10 for n >= 1.

G.f.: 5*(1+x)/(1-x).

E.g.f.: 10*exp(x) - 5.

a(n) = 5*A040000(n). (End)

Example

5.09901951359278483002822... = 5 + 1/(10 + 1/(10 + 1/(10 + 1/(10 + ...)))). - Harry J. Smith, Jun 03 2009

Maple

numtheory[cfrac](sqrt(26), 100, 'quotients'); # obsolete code updated by Alois P. Heinz, Feb 24 2018

Mathematica

ContinuedFraction[Sqrt[26], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5}, 120, {10}] (* Harvey P. Dale, Apr 22 2021 *)

Prog

(PARI) contfrac(sqrt(26)) \\ Harry J. Smith, Jun 03 2009 [Edited by M. F. Hasler, Feb 24 2018]
(PARI) A040020(n)=if(n, 10, 5) \\ M. F. Hasler, Feb 24 2018

Crossrefs

Cf. A010481 (decimal expansion), A041040/A041041 (convergents), A248253 (Egyptian fraction).

Cf. A040000, A010692.

Sequence in context: A346007 A135912 A200990 * A222181 A282172 A123337

Adjacent sequences: A040017 A040018 A040019 * A040021 A040022 A040023

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved