A197299 The Riemann primes of the theta type and index 3.

2, 3, 5, 7, 13, 17, 23, 31, 37, 41, 43, 47, 53, 59, 67, 73, 83, 89, 101, 103, 137, 163, 167, 179, 197, 211, 223, 239, 251, 277, 331, 379, 397, 431, 463, 467, 521, 577, 593, 601, 613, 617, 719, 809, 881, 919, 967, 1091, 1123, 1129, 1237, 1249, 1289

Offset

1,1

References

The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |theta(p^3)-p^3|, where theta(p) is the Chebyshev theta function.

Links

Dana Jacobsen, Table of n, a(n) for n = 1..85

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

Prog

(Perl) use ntheory ":all"; my($max, $f)=(0); forprimes { $f=abs(chebyshev_theta($_**3)-$_**3); if ($f > $max) { say; $max=$f; } } 1000; # Dana Jacobsen, Dec 28 2015

Crossrefs

Cf. A196669, A197187, A197297, A197298, A197300.

Sequence in context: A094317 A074834 A163998 * A089438 A155777 A262839

Adjacent sequences: A197296 A197297 A197298 * A197300 A197301 A197302

Keyword

nonn

Author

Michel Planat, Oct 13 2011

Extensions

More terms from Dana Jacobsen, Dec 28 2015

Status

approved