%I #20 Dec 03 2018 12:57:00
%S 2,3,5,7,11,13,17,29,59,67,97,103,149,151,233,251,277,311,313,479,643,
%T 719,919,967,1039,1373,1489,1553,1847,1973,1979,2663,2953,3323,3677,
%U 3691,4651,4663,4789
%N The Riemann primes of the psi type and index 3.
%C The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |psi(p^3)-p^3|, where psi(p) is the Chebyshev psi function.
%H M. Planat and P. Solé, <a href="http://arxiv.org/abs/1109.6489">Efficient prime counting and the Chebyshev primes</a>, arXiv:1109.6489 [math.NT], 2011.
%t ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
%t Reap[For[max=0; p=2, p < 1000, p = NextPrime[p], f = Abs[ChebyshevPsi[p^3] - p^3]; If[f > max, max = f; Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Dec 03 2018 *)
%o (Perl) use ntheory ":all"; my($max,$f)=(0); forprimes { $f=abs(chebyshev_psi($_**3)-$_**3); if ($f > $max) { say; $max=$f; } } 1000; # _Dana Jacobsen_, Dec 28 2015
%Y Cf. A196669, A197185, A197186, A197188.
%K nonn,more
%O 1,1
%A _Michel Planat_, Oct 11 2011
%E More terms from _Dana Jacobsen_, Dec 28 2015