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
Examples
8.53973422267356706546355086954657449503488853576511496187960113...
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
Programs
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Magma
SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*Exp(1); // G. C. Greubel, Aug 24 2018
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Mathematica
RealDigits[N[Pi*E,6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)
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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
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 Graciá Llorente, May 31 2024
Extensions
Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
Comments