A319229 a(n) is equal to the difference between the nearest integer to the imaginary part of the n-th zero of the Riemann zeta function and the n-th prime.

12, 18, 20, 23, 22, 25, 24, 24, 25, 21, 22, 19, 18, 18, 18, 14, 11, 11, 9, 6, 6, 4, 2, -2, -8, -9, -8, -11, -10, -12, -23, -26, -30, -28, -37, -37, -41, -44, -46, -50, -55, -53, -61, -62, -64, -64, -73, -83, -86, -86, -87, -92, -91, -100, -104, -107, -111, -112, -116, -118

Offset: 1

Author

Mark A. Thomas, Sep 14 2018

Keywords

• sign

Examples

			14 - 2 = 12, 21 - 3 = 18, 25 - 5 = 20.
		

Crossrefs

Cf. A000040, A002410.

Programs

PARI

lista(nn) = my(v=apply(round, lfunzeros(lzeta, nn))); vector(#v, n, v[n] - prime(n)); \\ Michel Marcus, Sep 14 2018

Formula

a(n) = A002410(n) - prime(n).