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.

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, 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, 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

Offset: 0

Author

Jean-François Alcover, May 19 2014

Keywords

• nonn
• cons

Examples

			0.495600180582143864254074285792498888...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.
• Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 2.17, p. 102.

Links

• Ovidiu Furdui, Problem 164, Missouri J. Math. Sci., Vol. 18, No. 2 (2006), p. 148; Solution, ibid., Vol. 19, No. 2 (2007), pp. 156-158.

Crossrefs

Cf. A064052, A082633, A153810, A242493.

Programs

Mathematica

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

Formula

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

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

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