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A040011 Continued fraction for sqrt(15).

%I A040011 #34 Aug 22 2025 16:04:56
%S A040011 3,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,
%T A040011 6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,
%U A040011 6,1,6,1,6,1,6,1,6,1,6,1,6
%N A040011 Continued fraction for sqrt(15).
%C A040011 Decimal expansion of 313/990. - _R. J. Mathar_, Aug 22 2025
%D A040011 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040011 Harry J. Smith, <a href="/A040011/b040011.txt">Table of n, a(n) for n = 0..20000</a>
%H A040011 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A040011 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A040011 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040011 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A040011 Multiplicative with a(2^e) = 6, and a(p^e) = 1 for an odd prime p.
%F A040011 Dirichlet g.f.: zeta(s) * (1 + 5/2^s). (End)
%F A040011 G.f.: (3 + x + 3*x^2)/(1 - x^2). - _Stefano Spezia_, Jul 26 2025
%e A040011 3.872983346207416885179265399... = 3 + 1/(1 + 1/(6 + 1/(1 + 1/(6 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p A040011 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040011 ContinuedFraction[Sqrt[15],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040011 PadRight[{3},120,{6,1}] (* _Harvey P. Dale_, Apr 14 2020 *)
%o A040011 (PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(15)); for (n=0, 20000, write("b040011.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A040011 Cf. A010472 (decimal expansion). A010687.
%K A040011 nonn,cofr,easy,mult,changed
%O A040011 0,1
%A A040011 _N. J. A. Sloane_