A010124 - OEIS

%I #35 Dec 27 2023 00:23:36

%S 4,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,

%T 1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,1,3,1,2,8,2,

%U 1,3,1,2,8,2,1,3,1,2,8,2,1

%N Continued fraction for sqrt(19).

%H Harry J. Smith, <a href="/A010124/b010124.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. J. van der Poorten, <a href="https://web.archive.org/web/*/http://www-centre.mpce.mq.edu.au/alfpapers/a075.pdf">An introduction to continued fractions</a>, Unpublished.

%H A. J. van der Poorten, <a href="/A007400/a007400_4.pdf">An introduction to continued fractions</a>, Unpublished [Cached copy]

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%e 4.358898943540673552236981983... = 4 + 1/(2 + 1/(1 + 1/(3 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 03 2009

%t ContinuedFraction[Sqrt[19],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(19)); for (n=0, 20000, write("b010124.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009

%Y Cf. A041028/A041029 (convergents).

%Y Cf. A010475 (decimal expansion).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_