A242610 - OEIS

%I #8 Mar 26 2022 10:17:12

%S 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 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 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 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 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.

%D Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 2.17, p. 102.

%H 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 j(n) = log(2)*n - (1-gamma)*n/log(n) - (1-gamma-gamma(1))*n/log(n)^2 + O(n/log(n)^3).

%F Equals -Integral_{x=0..1} frac(1/x)*log(x) dx (Furdui, 2007 and 2013). - _Amiram Eldar_, Mar 26 2022

%e 0.495600180582143864254074285792498888...

%t RealDigits[1 - EulerGamma - StieltjesGamma[1], 10, 100] // First

%Y Cf. A064052, A082633, A153810, A242493.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, May 19 2014