This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A040042 #37 Aug 25 2025 11:12:10
%S A040042 7,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
%T A040042 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
%U A040042 14,14,14,14,14,14,14,14,14
%N A040042 Continued fraction for sqrt(50) = 5*sqrt(2).
%D A040042 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040042 Harry J. Smith, <a href="/A040042/b040042.txt">Table of n, a(n) for n = 0..20000</a>
%H A040042 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040042 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040042 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040042 From _Elmo R. Oliveira_, Feb 07 2024: (Start)
%F A040042 a(n) = 14 = A010853(n) for n >= 1.
%F A040042 G.f.: 7*(1+x)/(1-x).
%F A040042 E.g.f.: 14*exp(x) - 7.
%F A040042 a(n) = 7*A040000(n). (End)
%e A040042 7.07106781186547524400844... = 7 + 1/(14 + 1/(14 + 1/(14 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 01 2009
%p A040042 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040042 ContinuedFraction[Sqrt[50],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)
%o A040042 (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 A040042 Cf. A010503 (decimal expansion), A041084/A041085 (convergents), A248275 (Egyptian fraction).
%Y A040042 Cf. A040000.
%K A040042 nonn,cofr,easy,changed
%O A040042 0,1
%A A040042 _N. J. A. Sloane_