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A242610 Decimal expansion of 1-gamma-gamma(1), a constant related to the asymptotic expansion of j(n), the counting function of "jagged" numbers, where gamma is Euler-Mascheroni constant and gamma(1) the first Stieltjes constant.

%I A242610 #12 Jul 31 2025 08:42:30
%S A242610 4,9,5,6,0,0,1,8,0,5,8,2,1,4,3,8,6,4,2,5,4,0,7,4,2,8,5,7,9,2,4,9,8,8,
%T A242610 8,8,0,9,5,5,7,7,0,0,2,3,9,4,4,1,4,3,5,3,7,9,3,2,3,9,3,2,4,8,5,6,5,3,
%U A242610 3,7,0,6,7,9,3,8,4,6,8,1,3,9,4,1,1,3,9,8,6,4,9,5,3,0,9,7,2,6,5,0
%N A242610 Decimal expansion of 1-gamma-gamma(1), a constant related to the asymptotic expansion of j(n), the counting function of "jagged" numbers, where gamma is Euler-Mascheroni constant and gamma(1) the first Stieltjes constant.
%D A242610 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.
%D A242610 Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 2.17, p. 102.
%H A242610 Ovidiu Furdui, <a href="https://doi.org/10.35834/2006/1802147">Problem 164</a>, Missouri J. Math. Sci., Vol. 18, No. 2 (2006), p. 148; <a href="https://doi.org/10.35834/mjms/1316092495">Solution</a>, ibid., Vol. 19, No. 2 (2007), pp. 156-158.
%F A242610 j(n) = log(2)*n - (1-gamma)*n/log(n) - (1-gamma-gamma(1))*n/log(n)^2 + O(n/log(n)^3).
%F A242610 Equals -Integral_{x=0..1} frac(1/x)*log(x) dx (Furdui, 2007 and 2013). - _Amiram Eldar_, Mar 26 2022
%F A242610 Equals Integral_{x=0..1} Integral_{y=0..1} frac(1/(x*y)) dx dy (Furdui, 2013, section 2.43, p. 106). - _Amiram Eldar_, Jul 31 2025
%e A242610 0.495600180582143864254074285792498888...
%t A242610 RealDigits[1 - EulerGamma - StieltjesGamma[1], 10, 100] // First
%Y A242610 Cf. A064052, A082633, A153810, A242493.
%K A242610 nonn,cons
%O A242610 0,1
%A A242610 _Jean-François Alcover_, May 19 2014