cp's OEIS Frontend

A040020 Continued fraction for sqrt(26).

%I A040020 #49 Aug 25 2025 11:08:36
%S A040020 5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%T A040020 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%U A040020 10,10,10,10,10,10,10,10,10
%N A040020 Continued fraction for sqrt(26).
%D A040020 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040020 Harry J. Smith, <a href="/A040020/b040020.txt">Table of n, a(n) for n = 0..20000</a>
%H A040020 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040020 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040020 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040020 From _Elmo R. Oliveira_, Feb 06 2024: (Start)
%F A040020 a(n) = 10 for n >= 1.
%F A040020 G.f.: 5*(1+x)/(1-x).
%F A040020 E.g.f.: 10*exp(x) - 5.
%F A040020 a(n) = 5*A040000(n). (End)
%e A040020 5.09901951359278483002822... = 5 + 1/(10 + 1/(10 + 1/(10 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p A040020 numtheory[cfrac](sqrt(26), 100, 'quotients'); # obsolete code updated by _Alois P. Heinz_, Feb 24 2018
%t A040020 ContinuedFraction[Sqrt[26],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040020 PadRight[{5},120,{10}] (* _Harvey P. Dale_, Apr 22 2021 *)
%o A040020 (PARI) contfrac(sqrt(26)) \\ _Harry J. Smith_, Jun 03 2009 [Edited by _M. F. Hasler_, Feb 24 2018]
%o A040020 (PARI) A040020(n)=if(n,10,5) \\ _M. F. Hasler_, Feb 24 2018
%Y A040020 Cf. A010481 (decimal expansion), A041040/A041041 (convergents), A248253 (Egyptian fraction).
%Y A040020 Cf. A040000, A010692.
%K A040020 nonn,cofr,easy,changed
%O A040020 0,1
%A A040020 _N. J. A. Sloane_