A019609 - OEIS

%I #63 Jun 01 2024 06:19:20

%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 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

%F Equals Product_{k>=0} ((k + 1)^(4*k + 3)/(k + 2)^(6*k + 5))*(((2*k + 3)*(k + 3))/(2*k + 1))^(2*k + 2). - _Antonio Graciá Llorente_, May 31 2024

%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