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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Examples

			5.09901951359278483002822... = 5 + 1/(10 + 1/(10 + 1/(10 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 03 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. A010481 (decimal expansion), A041040/A041041 (convergents), A248253 (Egyptian fraction).

Cf. A040000, A010692.

Programs

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 *)

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

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)