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

Author

Amiram Eldar, Jun 29 2021

Keywords

• nonn
• cons
• more

Comments

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

Examples

			-0.2432383428909807554150591354654623071783049...
		

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

• 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.

Crossrefs

Cf. A099769, A168218.

Formula

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