cp's OEIS Frontend

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.

A010169 Continued fraction for sqrt(98).

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%I A010169 #30 Nov 15 2023 01:15:58
%S A010169 9,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,
%T A010169 1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,1,8,1,18,
%U A010169 1,8,1,18,1,8,1,18,1,8,1,18
%N A010169 Continued fraction for sqrt(98).
%H A010169 Harry J. Smith, <a href="/A010169/b010169.txt">Table of n, a(n) for n = 0..20000</a>
%H A010169 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010169 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010169 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010169 From _Wesley Ivan Hurt_, Jun 23 2021: (Start)
%F A010169 a(n) = a(n-4).
%F A010169 a(0) = 9; a(n) = 7 + 6*(-1)^n + 5*cos(n*Pi/2) for n > 0. (End)
%F A010169 From _Amiram Eldar_, Nov 14 2023: (Start)
%F A010169 Multiplicative with a(2) = 8, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010169 Dirichlet g.f.: zeta(s) * (1 + 7/2^s + 5/2^(2*s-1)). (End)
%e A010169 9.89949493661166534161182106... = 9 + 1/(1 + 1/(8 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 12 2009
%t A010169 ContinuedFraction[Sqrt[98],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2011 *)
%t A010169 PadRight[{9},120,{18,1,8,1}] (* _Harvey P. Dale_, Dec 13 2015 *)
%o A010169 (PARI) { allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(98)); for (n=0, 20000, write("b010169.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 12 2009
%Y A010169 Cf. A010549 (decimal expansion).
%K A010169 nonn,cofr,easy,mult
%O A010169 0,1
%A A010169 _N. J. A. Sloane_