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

0,1

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

Table of n, a(n) for n=0..99.

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.

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

Example

0.495600180582143864254074285792498888...

Mathematica

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

Crossrefs

Cf. A064052, A082633, A153810, A242493.

Sequence in context: A200011 A200241 A243710 * A292484 A197418 A137807

Adjacent sequences: A242607 A242608 A242609 * A242611 A242612 A242613

Keyword

nonn,cons

Author

Jean-François Alcover, May 19 2014

Status

approved