A197298 The Riemann primes of the theta type and index 2.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 59, 73, 97, 107, 109, 139, 179, 233, 263, 277, 283, 337, 347, 409, 419, 547, 643, 683, 809, 811, 821, 823, 863, 983, 991, 997, 1031, 1193

Offset

1,1

Comments

The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |theta(p^2)-p^2|, where theta(p) is the Chebyshev theta function.

Links

Dana Jacobsen, Table of n, a(n) for n = 1..173

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

Prog

(Perl) use ntheory ":all"; my($max, $f)=(0); forprimes { $f=abs(chebyshev_theta($_**2)-$_**2); if ($f > $max) { say; $max=$f; } } 10000; # Dana Jacobsen, Dec 29 2015

Crossrefs

Cf. A196668, A197186, A197297, A197299, A197300.

Sequence in context: A268513 A256484 A238242 * A211654 A363998 A038612

Adjacent sequences: A197295 A197296 A197297 * A197299 A197300 A197301

Keyword

nonn

Author

Michel Planat, Oct 13 2011

Status

approved