Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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