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%I #31 Feb 16 2024 12:28:06
%S 7,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
%T 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
%U 14,14,14,14,14,14,14,14,14
%N Continued fraction for sqrt(50) = 5*sqrt(2).
%H Harry J. Smith, <a href="/A040042/b040042.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 07 2024: (Start)
%F a(n) = 14 for n >= 1.
%F G.f.: 7*(1+x)/(1-x).
%F E.g.f.: 14*exp(x) - 7.
%F a(n) = 7*A040000(n). (End)
%e 7.07106781186547524400844... = 7 + 1/(14 + 1/(14 + 1/(14 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 01 2009
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[50],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 47000); x=contfrac(sqrt(50)); for (n=0, 20000, write("b040042.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 01 2009
%Y Cf. A010503 (decimal expansion), A041084/A041085 (convergents), A248275 (Egyptian fraction).
%Y Cf. A040000.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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