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

1,1

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

Table of n, a(n) for n=1..39.

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 < 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 *)

Prog

(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

Crossrefs

Cf. A196669, A197185, A197186, A197188.

Sequence in context: A249644 A103144 A105909 * A086498 A211655 A359138

Adjacent sequences: A197184 A197185 A197186 * A197188 A197189 A197190

Keyword

nonn,more

Author

Michel Planat, Oct 11 2011

Extensions

More terms from Dana Jacobsen, Dec 28 2015

Status

approved