Search: id:A118292
Results 1-1 of 1 results found.

%I A118292
%S A118292 2,8,0,4,3,6,4,2,1,0,6,5,0,9,0,8,5,2,2,3,5,0,0,3,8,1,5,8,1,0,0,5,8,8,2,
%T A118292 7,0,9,2,6,0,4,4,4,1,0,8,4,7,9,7,2,1,9,2,3,6,3,9,8,7,9,7,4,1,5,2,5,6,9,
%U A118292 5,3,1,9,6,3,6,0,6,5,9,2,1,4,1,7,0,4,5,3,2,9,7,0,0,4,9,5,6,9,4,1,1,0,3
%N A118292 Decimal expansion of (Gamma[1/6]*Gamma[1/3])/(3*Sqrt[Pi]).
%C A118292 General formula (*Artur Jasinski*): Integrate[(1+x^(3n))/Sqrt[1-x^3],
               {x,0,1}] = G_3 * k_n = G_3*A146751(n)/A146752(n) = A118292*A146751(n)/
               A146752(n) where G_3 = (Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi) is the number 
               in the present entry. For numerators of k_n see A146752, for denominators 
               of k_n see A146753.
%C A118292 gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
%H A118292 Harry J. Smith, <a href="b118292.txt">Table of n, a(n) for n=1,...,4000</
               a>
%H A118292 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ButterflyCurve.html">Butterfly Curve</a>
%F A118292 Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/
               0403510] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 
               2008]
%e A118292 2.8043642106509085223...
%e A118292 2.8043642106509085223500381581005882709260444108479721923639879741525695... 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
%t A118292 RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (*Artur Jasinski*)
%o A118292 (PARI) { allocatemem(932245000); default(realprecision, 4080); x=gamma(1/
               3)^3/(2^(1/3)*sqrt(3)*Pi); for (n=1, 4000, d=floor(x); x=(x-d)*10; 
               write("b118292.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 20 2009]
%Y A118292 Cf. A146752, A146753
%Y A118292 Cf. A160323 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 09 2009]
%Y A118292 Sequence in context: A021785 A136664 A086728 this_sequence A160584 A011055 
               A020860
%Y A118292 Adjacent sequences: A118289 A118290 A118291 this_sequence A118293 A118294 
               A118295
%K A118292 nonn,cons
%O A118292 1,1
%A A118292 Eric Weisstein (eric(AT)weisstein.com), Apr 22, 2006
%E A118292 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 16 2008 at 
               the suggestion of R. J. Mathar
%E A118292 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009

Search completed in 0.001 seconds