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A040019 Continued fraction for sqrt(24).

%I A040019 #36 Aug 25 2025 11:07:17
%S A040019 4,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,
%T A040019 8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,
%U A040019 8,1,8,1,8,1,8,1,8,1,8,1,8
%N A040019 Continued fraction for sqrt(24).
%C A040019 Decimal expansion of 23/55. - _R. J. Mathar_, Aug 25 2025
%D A040019 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040019 Harry J. Smith, <a href="/A040019/b040019.txt">Table of n, a(n) for n = 0..20000</a>
%H A040019 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A040019 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A040019 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040019 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A040019 Multiplicative with a(2^e) = 8, and a(p^e) = 1 for an odd prime p.
%F A040019 Dirichlet g.f.: zeta(s) * (1 + 7/2^s). (End)
%F A040019 G.f.: (4 + x + 4*x^2)/(1 - x^2). - _Stefano Spezia_, Jul 26 2025
%e A040019 4.898979485566356196394568149... = 4 + 1/(1 + 1/(8 + 1/(1 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p A040019 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040019 ContinuedFraction[Sqrt[24],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040019 PadRight[{4},120,{8,1}] (* _Harvey P. Dale_, Oct 24 2022 *)
%o A040019 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(24)); for (n=0, 20000, write("b040019.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A040019 Cf. A010480 (decimal expansion), A010689.
%K A040019 nonn,cofr,easy,mult,changed
%O A040019 0,1
%A A040019 _N. J. A. Sloane_