A040033 - OEIS

%I #25 Dec 27 2023 00:40:04

%S 6,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,

%T 12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,

%U 3,12,3,12,3,12,3,12,3,12,3

%N Continued fraction for sqrt(40).

%H Harry J. Smith, <a href="/A040033/b040033.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).

%e 6.3245553203367586639977870... = 6 + 1/(3 + 1/(12 + 1/(3 + 1/(12 + ...)))). - _Harry J. Smith_, Jun 05 2009

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

%t ContinuedFraction[Sqrt[40],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)

%t LinearRecurrence[{0,1},{6,3,12},100] (* or *) PadRight[{6},100,{12,3}] (* _Harvey P. Dale_, Mar 03 2018 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 32000); x=contfrac(sqrt(40)); for (n=0, 20000, write("b040033.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 05 2009

%Y Cf. A010494 Decimal expansion. - _Harry J. Smith_, Jun 05 2009

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_