A019609 Decimal expansion of Pi*e.

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, 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, 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

Offset

1,1

Comments

Pi*e ~= 316211059661164487904100 / 37028208538575230865001. - Alexander R. Povolotsky, Aug 06 2009

Pi*e ~= 2*( Sum_{k>=1} (1/Product_{k=1..n}(2*k-1) ) + 725013737/1105744026 )^2. - Alexander R. Povolotsky, Aug 08 2009

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

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

Cf. A159822 (continued fraction for Pi*e).

Cf. also A000796 (Pi), A001113 (e).

Sequence in context: A011466 A154509 A081885 * A334502 A093341 A134973

Adjacent sequences: A019606 A019607 A019608 * A019610 A019611 A019612

Keyword

nonn,cons

Author

N. J. A. Sloane

Extensions

Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008

Status

approved