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%I #27 Nov 12 2023 05:55:17
%S 2,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,
%T 4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,
%U 4,1,4,1,4,1,4,1,4,1,4,1,4
%N Continued fraction for sqrt(8).
%H Harry J. Smith, <a href="/A040005/b040005.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 From _Amiram Eldar_, Nov 12 2023: (Start)
%F Multiplicative with a(2^e) = 4, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 3/2^s). (End)
%e 2.828427124746190097603377448... = 2 + 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, Jun 02 2009
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[8],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 04 2011 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(8)); for (n=0, 20000, write("b040005.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009
%Y Cf. A010466 (decimal expansion). - _Harry J. Smith_, Jun 02 2009
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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