A197187 The Riemann primes of the psi type and index 3.

2, 3, 5, 7, 11, 13, 17, 29, 59, 67, 97, 103, 149, 151, 233, 251, 277, 311, 313, 479, 643, 719, 919, 967, 1039, 1373, 1489, 1553, 1847, 1973, 1979, 2663, 2953, 3323, 3677, 3691, 4651, 4663, 4789

Offset: 1

Author

Michel Planat, Oct 11 2011

Keywords

• nonn
• more

Comments

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.

Links

• M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes, arXiv:1109.6489 [math.NT], 2011.

Crossrefs

Cf. A196669, A197185, A197186, A197188.

Programs

Mathematica

ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
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 *)

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

Extensions

More terms from Dana Jacobsen, Dec 28 2015