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 A010125 #40 Jul 26 2025 09:31:08
%S A010125 4,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,
%T A010125 1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,
%U A010125 1,2,1,1,8,1,1,2,1,1,8,1,1
%N A010125 Continued fraction for sqrt(21).
%D A010125 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010125 Harry J. Smith, <a href="/A010125/b010125.txt">Table of n, a(n) for n = 0..20000</a>
%H A010125 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A010125 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A010125 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A010125 a(n) = gcd(Fibonacci(n), Fibonacci(n-6)), n > 0. - _Gary Detlefs_, Dec 29 2010
%F A010125 G.f.: (4 + x + x^2 + 2*x^3 + x^4 + x^5 + 4*x^6)/(1 - x^6). - _Stefano Spezia_, Jul 26 2025
%e A010125 4.582575694955840006588047193... = 4 + 1/(1 + 1/(1 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 03 2009
%t A010125 ContinuedFraction[Sqrt[21],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A010125 PadRight[{4},120,{8,1,1,2,1,1}] (* _Harvey P. Dale_, May 16 2020 *)
%o A010125 (PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(21)); for (n=0, 20000, write("b010125.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A010125 Cf. A041032/A041033 (convergents), A010477 (decimal expansion).
%K A010125 nonn,cofr,easy
%O A010125 0,1
%A A010125 _N. J. A. Sloane_