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

1,1

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

Table of n, a(n) for n=1..52.

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 { $f=abs(chebyshev_theta($_**4)-$_**4); if ($f > $max) { say; $max=$f; } } 1000; # Dana Jacobsen, Dec 28 2015

Crossrefs

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

Sequence in context: A065722 A335331 A279956 * A028864 A342063 A067903

Adjacent sequences: A197297 A197298 A197299 * A197301 A197302 A197303

Keyword

nonn

Author

Michel Planat, Oct 13 2011

Extensions

More terms from Dana Jacobsen, Dec 28 2015

Status

approved