%I #6 Jun 09 2023 01:30:33
%S 7,2,8,6,9,3,9,1,7,0,0,3,9,3,0,6,0,5,9,3,7,6,0,5,8,9,1,0,2,0,2,9,1,8,
%T 0,0,4,1,7,5,0,2,7,1,8,8,1,2,9,2,2,2,9,9,8,9,1,3,6,9,0,0,5,4,2,5,2,7,
%U 2,2,7,1,9,2,5,2,3,3,5,8,6,9,6,4,2,6,9,7,4,4,2,3,8,8,6,5,3,7,8,6,0,4,5,5,9
%N Decimal expansion of Sum_{k>=1} (H(k) - log(k) - gamma)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620).
%H Iaroslav V. Blagouchine, <a href="https://doi.org/10.1016/j.jnt.2015.06.012">Expansions of generalized Euler's constants into the series of polynomials in Pi^(-2) and into the formal enveloping series with rational coefficients only</a>, Journal of Number Theory, Vol. 158 (2016), pp. 365-396.
%H Ovidiu Furdui, <a href="http://www.jstor.org/stable/27646421">Problem 844</a>, Problems and Solutions, The College Mathematics Journal, Vol. 38, No. 1 (2007), p. 61; <a href="http://www.jstor.org/stable/27646572">Infinite sums and Euler's constant</a>, Solution to Problem 844, ibid., Vol. 39, No. 1 (2008), pp. 71-72.
%F Equals -gamma_1 - gamma^2/2 + Pi^2/12, where gamma_1 is the 1st Stieltjes constant (A082633).
%e 0.72869391700393060593760589102029180041750271881292...
%t RealDigits[-StieltjesGamma[1] - EulerGamma^2/2 + Pi^2/12, 10, 120][[1]]
%Y Cf. A001008, A001620, A002805, A072691, A082633, A363539, A363540.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Jun 09 2023