A197300 The Riemann primes of the theta type and index 4.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 61, 67, 71, 89, 97, 109, 137, 139, 167, 173, 191, 223, 229, 239, 241, 269, 271, 293, 311, 331, 347, 367, 401, 431, 433, 457, 503, 509, 571, 577, 661, 709, 719, 733, 739, 797, 911, 919, 1009

Offset: 1

Author

Michel Planat, Oct 13 2011

Keywords

• nonn

Comments

The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |theta(p^4)-p^4|, where theta(p) is the Chebyshev theta function, theta(x) = sum_{primes p <=x } log p.

Links

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

Crossrefs

Cf. A035158, A196670, A197188, A197297, A197298, A197299.

Programs

Perl

use ntheory ":all"; my($max,$f)=(0); forprimes { $f=abs(chebyshev_theta($**4)-$**4); if ($f > $max) { say; $max=$f; } } 1000; # Dana Jacobsen, Dec 28 2015

Extensions

More terms from Dana Jacobsen, Dec 28 2015