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Continued fraction for sqrt(26).
8

%I #43 Feb 16 2024 12:28:12

%S 5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,

%T 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,

%U 10,10,10,10,10,10,10,10,10

%N Continued fraction for sqrt(26).

%H Harry J. Smith, <a href="/A040020/b040020.txt">Table of n, a(n) for n = 0..20000</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Elmo R. Oliveira_, Feb 06 2024: (Start)

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

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

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

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

%e 5.09901951359278483002822... = 5 + 1/(10 + 1/(10 + 1/(10 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 03 2009

%p numtheory[cfrac](sqrt(26), 100, 'quotients'); # obsolete code updated by _Alois P. Heinz_, Feb 24 2018

%t ContinuedFraction[Sqrt[26],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{5},120,{10}] (* _Harvey P. Dale_, Apr 22 2021 *)

%o (PARI) contfrac(sqrt(26)) \\ _Harry J. Smith_, Jun 03 2009 [Edited by _M. F. Hasler_, Feb 24 2018]

%o (PARI) A040020(n)=if(n,10,5) \\ _M. F. Hasler_, Feb 24 2018

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

%Y Cf. A040000.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_