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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A196668, A197185, A197187, A197188.

Sequence in context: A132146 A139827 A362035 * A063118 A267540 A141068

Adjacent sequences: A197183 A197184 A197185 * A197187 A197188 A197189

Keyword

nonn

Author

Michel Planat, Oct 11 2011

Extensions

More terms from Dana Jacobsen, Dec 29 2015

Status

approved