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%I #29 Nov 13 2023 07:11:31
%S 8,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,
%T 16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,
%U 1,16,1,16,1,16,1,16,1,16,1
%N Continued fraction for sqrt(80).
%H Harry J. Smith, <a href="/A040071/b040071.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(n) = 4^(1+(-1)^n) for n>0, a(0)=8. - _Bruno Berselli_, Dec 29 2015
%F From _Amiram Eldar_, Nov 13 2023: (Start)
%F Multiplicative with a(2^e) = 16, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 15/2^s). (End)
%e 8.9442719099991587856366946... = 8 + 1/(1 + 1/(16 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 09 2009
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[80],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)
%t PadRight[{8},120,{16,1}] (* _Harvey P. Dale_, Apr 16 2022 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 26000); x=contfrac(sqrt(80)); for (n=0, 20000, write("b040071.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 09 2009
%Y Cf. A010532 (decimal expansion).
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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