OFFSET
1,1
COMMENTS
Not known to be irrational (though of course conjectured transcendental), see e.g. Klee & Wagon. - Charles R Greathouse IV, Jul 23 2015
REFERENCES
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.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..20000
FORMULA
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
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 GraciĆ” Llorente, May 31 2024
EXAMPLE
8.53973422267356706546355086954657449503488853576511496187960113...
MATHEMATICA
RealDigits[N[Pi*E, 6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)
PROG
(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
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*Exp(1); // G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
STATUS
approved