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 A010123 #47 Jul 26 2025 08:04:23
%S A010123 3,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,
%T A010123 2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,
%U A010123 6,1,2,1,6,1,2,1,6,1,2,1,6
%N A010123 Continued fraction for sqrt(14).
%D A010123 Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 56. [From _Olivier Gérard_, May 22 2009]
%D A010123 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010123 Harry J. Smith, <a href="/A010123/b010123.txt">Table of n, a(n) for n = 0..20000</a>
%H A010123 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010123 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010123 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010123 a(n) = 1 + floor((n+2)/4) - floor((n+1)/4) + 5*(floor((n+4)/4) - floor((n+3)/4)) for n > 0. - _Wesley Ivan Hurt_, Apr 10 2017
%F A010123 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010123 Multiplicative with a(2) = 2, a(2^e) = 6 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010123 Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 1/2^(2*s-2)). (End)
%F A010123 G.f.: (3 + x + 2*x^2 + x^3 + 3*x^4)/(1 - x^4). - _Stefano Spezia_, Jul 26 2025
%e A010123 3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))). - _Harry J. Smith_, Jun 02 2009
%t A010123 ContinuedFraction[Sqrt[14],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A010123 PadRight[{3},120,{6,1,2,1}] (* _Harvey P. Dale_, Jan 16 2017 *)
%o A010123 (PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009
%Y A010123 Cf. A010471 (decimal expansion).
%K A010123 nonn,cofr,easy,mult
%O A010123 0,1
%A A010123 _N. J. A. Sloane_