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 A010137 #30 Jul 27 2025 10:05:25
%S A010137 6,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,
%T A010137 1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,1,5,1,12,
%U A010137 1,5,1,12,1,5,1,12,1,5,1,12
%N A010137 Continued fraction for sqrt(47).
%D A010137 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010137 Harry J. Smith, <a href="/A010137/b010137.txt">Table of n, a(n) for n = 0..20000</a>
%H A010137 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010137 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010137 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010137 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010137 Multiplicative with a(2) = 5, a(2^e) = 12 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010137 Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-2) + 7/4^s). (End)
%F A010137 G.f.: (6 + x + 5*x^2 + x^3 + 6*x^4)/(1 - x^4). - _Stefano Spezia_, Jul 27 2025
%e A010137 6.85565460040104412493587144... = 6 + 1/(1 + 1/(5 + 1/(1 + 1/(12 + ...)))). - _Harry J. Smith_, Jun 06 2009
%t A010137 ContinuedFraction[Sqrt[47],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)
%o A010137 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(47)); for (n=0, 20000, write("b010137.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 06 2009
%Y A010137 Cf. A010501 (decimal expansion).
%K A010137 nonn,cofr,easy,mult
%O A010137 0,1
%A A010137 _N. J. A. Sloane_