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 A010132 #34 Jul 27 2025 04:19:18
%S A010132 5,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,
%T A010132 1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,
%U A010132 1,4,1,10,1,4,1,10,1,4,1,10
%N A010132 Continued fraction for sqrt(34).
%D A010132 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010132 Harry J. Smith, <a href="/A010132/b010132.txt">Table of n, a(n) for n = 0..20000</a>
%H A010132 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010132 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010132 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010132 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010132 Multiplicative with a(2) = 4, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010132 Dirichlet g.f.: zeta(s) * (1 + 3/2^(2*s-1) + 3/2^s). (End)
%F A010132 G.f.: (5 + x + 4*x^2 + x^3 + 5*x^4)/(1 - x^4). - _Stefano Spezia_, Jul 27 2025
%e A010132 5.83095189484530047087415287... = 5 + 1/(1 + 1/(4 + 1/(1 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009
%t A010132 ContinuedFraction[Sqrt[34],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%o A010132 (PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(34)); for (n=0, 20000, write("b010132.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 04 2009
%Y A010132 Cf. A010489 (decimal expansion).
%K A010132 nonn,cofr,easy,mult
%O A010132 0,1
%A A010132 _N. J. A. Sloane_