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%I #27 Aug 03 2024 17:09:51
%S 6,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,
%T 12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,2,12,2,
%U 2,12,2,2,12,2,2,12,2,2,12
%N Continued fraction for sqrt(41).
%H Harry J. Smith, <a href="/A010133/b010133.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_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F From _Elmo R. Oliveira_, Aug 03 2024: (Start)
%F G.f.: 2*(3 + x + x^2 + 3*x^3)/((1 - x)*(1 + x + x^2)).
%F a(n) = a(n-3), n > 3. (End)
%e 6.40312423743284868648821767... = 6 + 1/(2 + 1/(2 + 1/(12 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 05 2009
%t ContinuedFraction[Sqrt[41],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(41)); for (n=0, 20000, write("b010133.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 05 2009
%Y Cf. A010495 Decimal expansion. - _Harry J. Smith_, Jun 05 2009
%Y Cf. A041068/A041069 (convergents), A248267 (Egyptian fraction).
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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