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 A010131 #36 Jul 26 2025 12:48:54
%S A010131 5,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,
%T A010131 1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,1,2,1,10,
%U A010131 1,2,1,10,1,2,1,10,1,2,1,10
%N A010131 Continued fraction for sqrt(33).
%D A010131 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010131 Harry J. Smith, <a href="/A010131/b010131.txt">Table of n, a(n) for n = 0..20000</a>
%H A010131 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010131 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010131 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010131 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010131 Multiplicative with a(2) = 2, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010131 Dirichlet g.f.: zeta(s) * (1 + 1/2^(2*s-3) + 1/2^s). (End)
%F A010131 G.f.: (5 + x + 2*x^2 + x^3 + 5*x^4)/(1 - x^4). - _Stefano Spezia_, Jul 26 2025
%e A010131 5.74456264653802865985061146... = 5 + 1/(1 + 1/(2 + 1/(1 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009
%t A010131 ContinuedFraction[Sqrt[33],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%t A010131 LinearRecurrence[{0,0,0,1},{5,1,2,1,10},100] (* or *) PadRight[{5},100,{10,1,2,1}] (* _Harvey P. Dale_, Dec 31 2017 *)
%o A010131 (PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(33)); for (n=0, 20000, write("b010131.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 04 2009
%Y A010131 Cf. A010488 (decimal expansion).
%K A010131 nonn,cofr,easy,mult
%O A010131 0,1
%A A010131 _N. J. A. Sloane_