A197297 The Riemann primes of the theta type and index 1.

2, 5, 7, 11, 17, 29, 37, 41, 53, 59, 97, 127, 137, 149, 191, 223, 307, 331, 337, 347, 419, 541, 557, 809, 967, 1009, 1213, 1277, 1399, 1409, 1423, 1973, 2203, 2237, 2591, 2609, 2617, 2633, 2647, 2657, 3163, 3299, 4861, 4871, 4889, 4903, 4931, 5381, 7411

Offset

1,1

Comments

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

Links

Dana Jacobsen, Table of n, a(n) for n = 1..744

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

L. Schoenfeld, Sharper bounds for the Chebyshev functions theta(x) and psi(x). II, Math. Comp. 30 (1976) 337-360.

Prog

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

Crossrefs

Cf. A196667, A197185, A197298, A197299, A197300.

Sequence in context: A019396 A153767 A038973 * A172527 A265817 A045349

Adjacent sequences: A197294 A197295 A197296 * A197298 A197299 A197300

Keyword

nonn

Author

Michel Planat, Oct 13 2011

Status

approved