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%I #57 Mar 30 2024 12:19:50
%S 8,5,3,9,7,3,4,2,2,2,6,7,3,5,6,7,0,6,5,4,6,3,5,5,0,8,6,9,5,4,6,5,7,4,
%T 4,9,5,0,3,4,8,8,8,5,3,5,7,6,5,1,1,4,9,6,1,8,7,9,6,0,1,1,3,0,1,7,9,2,
%U 2,8,6,1,1,1,5,7,3,3,0,8,0,7,5,7,2,5,6,3,8,6,9,7,1,0,4,7,3,9,4
%N Decimal expansion of Pi*e.
%C Pi*e ~= 316211059661164487904100 / 37028208538575230865001. - _Alexander R. Povolotsky_, Aug 06 2009
%C Pi*e ~= 2*( Sum_{k>=1} (1/Product_{k=1..n}(2*k-1) ) + 725013737/1105744026 )^2. - _Alexander R. Povolotsky_, Aug 08 2009
%C Not known to be irrational (though of course conjectured transcendental), see e.g. Klee & Wagon. - _Charles R Greathouse IV_, Jul 23 2015
%D Victor Klee and Stan Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory, Mathematical Association of America (1991). Problem 22, p. 243.
%H Harry J. Smith, <a href="/A019609/b019609.txt">Table of n, a(n) for n = 1..20000</a>
%F Limit_{k->oo} 4k/u(k)^2 where u(1)=0, u(2)=1, u(k+2) = u(k+1) + u(k)/(2k). - _Benoit Cloitre_, Aug 14 2003
%e 8.53973422267356706546355086954657449503488853576511496187960113...
%t RealDigits[N[Pi*E,6! ]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 18 2009 *)
%o (PARI) default(realprecision, 20080); x=Pi*exp(1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019609.txt", n, " ", d)); \\ _Harry J. Smith_, Apr 27 2009
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*Exp(1); // _G. C. Greubel_, Aug 24 2018
%Y Cf. A159822 (continued fraction for Pi*e).
%Y Cf. also A000796 (Pi), A001113 (e).
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_
%E Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
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