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A197297
The Riemann primes of the theta type and index 1.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Planat, Oct 13 2011
STATUS
approved