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).

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Iaroslav V. Blagouchine, Expansions of generalized Euler's constants into the series of polynomials in Pi^(-2) and into the formal enveloping series with rational coefficients only, Journal of Number Theory, Vol. 158 (2016), pp. 365-396.

Ovidiu Furdui, Problem 844, Problems and Solutions, The College Mathematics Journal, Vol. 38, No. 1 (2007), p. 61; Infinite sums and Euler's constant, Solution to Problem 844, ibid., Vol. 39, No. 1 (2008), pp. 71-72.

Formula

Equals -gamma_1 - gamma^2/2 + Pi^2/12, where gamma_1 is the 1st Stieltjes constant (A082633).

Example

0.72869391700393060593760589102029180041750271881292...

Mathematica

RealDigits[-StieltjesGamma[1] - EulerGamma^2/2 + Pi^2/12, 10, 120][[1]]

Crossrefs

Cf. A001008, A001620, A002805, A072691, A082633, A363539, A363540.

Sequence in context: A198564 A259072 A107311 * A048836 A198673 A086236

Adjacent sequences: A363535 A363536 A363537 * A363539 A363540 A363541

Keyword

nonn,cons

Author

Amiram Eldar, Jun 09 2023

Status

approved