A181110 Decimal expansion of 1/zeta(2) - 1/e^gamma, where gamma is the Euler-Mascheroni constant and zeta(2) = Pi^2/6.

0, 4, 6, 4, 6, 7, 6, 1, 8, 2, 8, 7, 1, 4, 1, 4, 5, 8, 8, 3, 9, 1, 3, 3, 5, 6, 4, 4, 6, 7, 4, 8, 5, 0, 4, 6, 6, 6, 0, 4, 4, 2, 2, 6, 1, 1, 0, 8, 3, 2, 6, 1, 2, 4, 9, 1, 9, 4, 9, 5, 1, 1, 5, 3, 1, 9, 9, 5, 0, 7, 5, 8, 6, 9, 9, 1, 2, 7, 0, 1, 0, 0, 1, 4, 3, 8, 4, 4, 8, 4, 6, 1, 9, 5, 1, 6, 6, 6, 6, 9, 1, 4

Offset: 0

Author

Jonathan Vos Post, Oct 03 2010

Keywords

• cons
• nonn

Comments

Zeta(2) is A013661 and e^gamma is A073004.

Number theory use in Cellarosi et al., p. 9. Abstract: "We present a limit theorem describing the behavior of a probabilistic model for squarefree numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval [0,1]. We also provide estimates for the error term in the limit theorem."

Examples

			0.046467618287141458839133564467485...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Francesco Cellarosi, Yakov G. Sinai, Non-Standard Limit Theorems in Number Theory, arXiv:1010.0035 [math.PR], 2010.

Crossrefs

Cf. A001620, A013661.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); 6/Pi(R)^2 - Exp(-EulerGamma(R)); // G. C. Greubel, Sep 06 2018

Mathematica

Join[{0}, RealDigits[1/Zeta[2] - Exp[-EulerGamma], 10, 100][[1]]] (* G. C. Greubel, Sep 06 2018 *)

PARI

1/zeta(2) - exp(-Euler) \\ Charles R Greathouse IV, Mar 10 2016

Formula

Equals A059956 - A080130.

Extensions

Offset and leading zeros normalized by R. J. Mathar, Oct 05 2010