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%I #20 Sep 08 2022 08:45:54
%S 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,
%T 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,
%U 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
%N Decimal expansion of 1/zeta(2) - 1/e^gamma, where gamma is the Euler-Mascheroni constant and zeta(2) = Pi^2/6.
%C Zeta(2) is A013661 and e^gamma is A073004.
%C 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."
%H G. C. Greubel, <a href="/A181110/b181110.txt">Table of n, a(n) for n = 0..10000</a>
%H Francesco Cellarosi, Yakov G. Sinai, <a href="http://arxiv.org/abs/1010.0035">Non-Standard Limit Theorems in Number Theory</a>, arXiv:1010.0035 [math.PR], 2010.
%F Equals A059956 - A080130.
%e 0.046467618287141458839133564467485...
%t Join[{0}, RealDigits[1/Zeta[2] - Exp[-EulerGamma], 10, 100][[1]]] (* _G. C. Greubel_, Sep 06 2018 *)
%o (PARI) 1/zeta(2) - exp(-Euler) \\ _Charles R Greathouse IV_, Mar 10 2016
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 6/Pi(R)^2 - Exp(-EulerGamma(R)); // _G. C. Greubel_, Sep 06 2018
%Y Cf. A001620, A013661.
%K cons,nonn
%O 0,2
%A _Jonathan Vos Post_, Oct 03 2010
%E Offset and leading zeros normalized by _R. J. Mathar_, Oct 05 2010
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