A217598 Decimal expansion of the coefficient of asymptotic expression of m(n), the number of multiplicative compositions of n.

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

Offset: 0

Author

Jean-François Alcover, Mar 19 2013

Keywords

• nonn
• cons

Comments

From Amiram Eldar, Oct 16 2020: (Start)

Equals -1/(rho * zeta'(rho)), where rho is the root of zeta(rho) = 2 (A107311).

Equals lim_{k->oo} A173382(k)/k^rho. (End)

Examples

			0.318173652...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 293.

Crossrefs

Cf. A074206, A107311 (rho), A173382.

Programs

Mathematica

rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> 100]; RealDigits[-1/(rho*Zeta'[rho])] // First

PARI

a217598={my(rho=solve(x=1.1,2,zeta(x)-2));-1/(rho*zeta'(rho))} \\ Hugo Pfoertner, Oct 16 2020