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 A010126 #37 Jul 26 2025 09:31:12
%S A010126 4,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,
%T A010126 2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,
%U A010126 2,4,2,1,8,1,2,4,2,1,8,1,2
%N A010126 Continued fraction for sqrt(22).
%D A010126 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010126 Harry J. Smith, <a href="/A010126/b010126.txt">Table of n, a(n) for n = 0..20000</a>
%H A010126 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010126 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010126 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A010126 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010126 Multiplicative with a(2^e) = 2, a(3^e) = 4, and a(p^e) = 1 for p >= 5.
%F A010126 Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 1/3^(s-1)). (End)
%F A010126 G.f.: (4 + x + 2*x^2 + 4*x^3 + 2*x^4 + x^5 + 4*x^6)/(1 - x^6). - _Stefano Spezia_, Jul 26 2025
%e A010126 4.690415759823429554565630113... = 4 + 1/(1 + 1/(2 + 1/(4 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 03 2009
%t A010126 ContinuedFraction[Sqrt[22],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A010126 PadRight[{4},120,{8,1,2,4,2,1}] (* _Harvey P. Dale_, Jul 02 2019 *)
%o A010126 (PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(22)); for (n=0, 20000, write("b010126.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A010126 Cf. A041034/A041035 (convergents), A248250 (Egyptian fraction), A010478 (decimal expansion).
%K A010126 nonn,cofr,easy,mult
%O A010126 0,1
%A A010126 _N. J. A. Sloane_