A345928 Decimal expansion of Integral_{x>=0} (zeta(x)-1) dx (negated).

2, 4, 3, 2, 3, 8, 3, 4, 2, 8, 9, 0, 9, 8, 0, 7, 5, 5, 4, 1, 5, 0, 5, 9, 1, 3, 5, 4, 6, 5, 4, 6, 2, 3, 0, 7, 1, 7, 8, 3, 0, 4, 9

Offset

0,1

Comments

Robinson (1980) conjectured and Newman and Widder (1981) proved that this integral is equal to the limit given in the Formula section.

References

Murray S. Klamkin (ed.), Problems in Applied Mathematics: Selections from SIAM Review, Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990, pp. 281-282.

Links

Table of n, a(n) for n=0..42.

H. P. Robinson, A Conjectured Limit, Problem 80-7, SIAM Review, Vol. 22, No. 2 (1980), p. 229; D. J. Newman and D. V. Widder, Solution, ibid., Vol. 23, No. 2 (1981), pp. 256-257.

Formula

Equals lim_{n->oo} (Sum_{k=2..n} 1/log(k) - Integral_{x=0..n} (1/log(x)) dx).

Example

-0.2432383428909807554150591354654623071783049...

Crossrefs

Cf. A099769, A168218.

Sequence in context: A005681 A049848 A152026 * A060806 A320044 A329876

Adjacent sequences: A345925 A345926 A345927 * A345929 A345930 A345931

Keyword

nonn,cons,more

Author

Amiram Eldar, Jun 29 2021

Status

approved