A040007 - OEIS

%I #33 Jan 18 2025 18:34:20

%S 3,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,

%T 6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,6,3,

%U 6,3,6,3,6,3,6,3,6,3,6,3

%N Continued fraction for sqrt(11).

%C Eventual period is (3,6). - _Zak Seidov_, Mar 05 2011

%D Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §4.4 Powers and Roots, p. 144.

%H Harry J. Smith, <a href="/A040007/b040007.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 _Stefano Spezia_, Jan 18 2025: (Start)

%F G.f.: 3*(1 + x + x^2)/(1 - x^2).

%F E.g.f.: 3*(2*cosh(x) + sinh(x) - 1). (End)

%e 3.316624790355399849114932736... = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + ...)))). - _Harry J. Smith_, Jun 02 2009

%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

%t ContinuedFraction[Sqrt[11],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{3},120,{6,3}] (* _Harvey P. Dale_, Jan 18 2025 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(11)); for (n=0, 20000, write("b040007.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009

%Y Cf. A010468.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_