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 A040015 #31 Aug 25 2025 11:07:54
%S A040015 4,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,
%T A040015 8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,8,2,
%U A040015 8,2,8,2,8,2,8,2,8,2,8,2,8
%N A040015 Continued fraction for sqrt(20).
%C A040015 Decimal expansion of 212/495. - _R. J. Mathar_, Aug 25 2025
%D A040015 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040015 Harry J. Smith, <a href="/A040015/b040015.txt">Table of n, a(n) for n = 0..20000</a>
%H A040015 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040015 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040015 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040015 G.f.: 2*(2 + x + 2*x^2)/(1 - x^2). - _Stefano Spezia_, Jul 26 2025
%e A040015 4.472135954999579392818347337... = 4 + 1/(2 + 1/(8 + 1/(2 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p A040015 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040015 ContinuedFraction[Sqrt[20],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040015 PadRight[{4},120,{8,2}] (* _Harvey P. Dale_, Jul 17 2023 *)
%o A040015 (PARI) { allocatemem(932245000); default(realprecision, 26000); x=contfrac(sqrt(20)); for (n=0, 20000, write("b040015.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A040015 Cf. A010476 (Decimal expansion), A010698.
%K A040015 nonn,cofr,easy,changed
%O A040015 0,1
%A A040015 _N. J. A. Sloane_