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%I #43 Apr 12 2021 00:07:44
%S 28,63,125,213,362,489,696,823,1104,1443,1642,2089,2433,2616,3060,
%T 3555,4103,4396,5072,5477,5792,6550,7033,7781,8614,9342,9749,10258,
%U 10773,11449,13173,13814,14682,15433,16669,17262,18248,19363,20269
%N 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.
%C Empirical: a(n) ~ 2*Pi*n^2.
%H Simon Plouffe, <a href="/A342756/b342756.txt">Table of n, a(n) for n = 1..100000</a>
%H David Platt, <a href="https://www.lmfdb.org/zeros/zeta/">Zeros of the Zeta function</a>.
%H David Platt, <a href="https://doi.org/10.1090/S0025-5718-2014-02884-6">Computing pi(x) analytically</a>, Mathematics of computation, 84 (2015), 1521-1535.
%H S. Plouffe, <a href="https://vixra.org/pdf/1907.0108v8.pdf">Pi, the primes and the Lambert W function</a> [Slides of a talk]
%e z(1) = 14.134... and prime(1) = 2, a(1) = round(14.134...*2) = 28.
%K nonn
%O 1,1
%A _Simon Plouffe_, Apr 11 2021