A197185 The Riemann primes of the psi type and index 1.

2, 59, 73, 97, 109, 113, 199, 283, 463, 467, 661, 1103, 1109, 1123, 1129, 1321, 1327, 1423, 2657, 2803, 2861, 3299, 5381, 5881, 6373, 6379, 9859, 9931, 9949, 10337, 10343, 11777, 19181, 19207, 19373, 24107, 24109, 24113, 24121, 24137, 42751, 42793, 42797

Offset

1,1

Comments

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

Links

Dana Jacobsen, Table of n, a(n) for n = 1..583

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

L. Schoenfeld, Sharper bounds for the Chebyshev functions theta(x) and psi(x). II, Math. Comp. 30 (1975) 337-360.

Mathematica

ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
Reap[For[max=0; p=2, p<50000, p = NextPrime[p], f = Abs[ChebyshevPsi[p]-p]; 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 { $f=abs(chebyshev_psi($_)-$_); if ($f > $max) { say; $max=$f; } } 10000; # Dana Jacobsen, Dec 29 2015

Crossrefs

Cf. A196667, A197186, A197187, A197188.

Sequence in context: A244269 A195325 A195329 * A232848 A215393 A141869

Adjacent sequences: A197182 A197183 A197184 * A197186 A197187 A197188

Keyword

nonn

Author

Michel Planat, Oct 11 2011

Status

approved