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