cp's OEIS Frontend

A363538 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).

%I A363538 #10 Apr 27 2025 03:22:54
%S A363538 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 A363538 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 A363538 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 A363538 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 A363538 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 A363538 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 A363538 Equals -gamma_1 - gamma^2/2 + Pi^2/12, where gamma_1 is the 1st Stieltjes constant (A082633).
%e A363538 0.72869391700393060593760589102029180041750271881292...
%t A363538 RealDigits[-StieltjesGamma[1] - EulerGamma^2/2 + Pi^2/12, 10, 120][[1]]
%Y A363538 Cf. A001008, A001620, A002805, A072691, A082633, A363539, A363540.
%K A363538 nonn,cons
%O A363538 0,1
%A A363538 _Amiram Eldar_, Jun 09 2023