A342756 Rounded value of z(n)*prime(n), where z(n) = imaginary part of n-th nontrivial zero of the Zeta function and prime(n) = n-th prime.

28, 63, 125, 213, 362, 489, 696, 823, 1104, 1443, 1642, 2089, 2433, 2616, 3060, 3555, 4103, 4396, 5072, 5477, 5792, 6550, 7033, 7781, 8614, 9342, 9749, 10258, 10773, 11449, 13173, 13814, 14682, 15433, 16669, 17262, 18248, 19363, 20269

Offset: 1

Author

Simon Plouffe, Apr 11 2021

Keywords

• nonn

Comments

Empirical: a(n) ~ 2*Pi*n^2.

Examples

			z(1) = 14.134... and prime(1) = 2, a(1) = round(14.134...*2) = 28.
		

Links

• Simon Plouffe, Table of n, a(n) for n = 1..100000
• David Platt, Zeros of the Zeta function.
• David Platt, Computing pi(x) analytically, Mathematics of computation, 84 (2015), 1521-1535.
• S. Plouffe, Pi, the primes and the Lambert W function [Slides of a talk]