A197186 The Riemann primes of the psi type and index 2.

2, 17, 31, 41, 53, 101, 109, 127, 139, 179, 397, 419, 547, 787, 997, 1031, 1229, 1801, 1811, 2099, 2237, 2417, 2423, 2657, 3163, 3203, 3517, 3581, 3583, 3931, 4241, 5503, 5507, 5557, 6079, 8087, 8719, 10433, 10487, 13399, 13411, 19309, 22303, 22307, 22613

Offset: 1

Author

Michel Planat, Oct 11 2011

Keywords

• nonn

Comments

The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |psi(p^2)-p^2|, where psi(p) is the Chebyshev psi function.

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..84
• M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes, arXiv:1109.6489 [math.NT], 2011.

Crossrefs

Cf. A196668, A197185, A197187, A197188.

Programs

Mathematica

ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
Reap[For[max=0; p=2, p < 2000, p = NextPrime[p], f = Abs[ChebyshevPsi[p^2] - p^2]; 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 { $f=abs(chebyshev_psi($**2)-$**2); if ($f > $max) { say; $max=$f; } } 10000; # Dana Jacobsen, Dec 29 2015

Extensions

More terms from Dana Jacobsen, Dec 29 2015