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A197185 The Riemann primes of the psi type and index 1. 5
2, 59, 73, 97, 109, 113, 199, 283, 463, 467, 661, 1103, 1109, 1123, 1129, 1321, 1327, 1423, 2657, 2803, 2861, 3299, 5381, 5881, 6373, 6379, 9859, 9931, 9949, 10337, 10343, 11777, 19181, 19207, 19373, 24107, 24109, 24113, 24121, 24137, 42751, 42793, 42797 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |psi(p)-p|, where psi(p) is the Chebyshev psi function.
LINKS
M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes arXiv:1109.6489 [math.NT], 2011.
L. Schoenfeld, Sharper bounds for the Chebyshev functions theta(x) and psi(x). II, Math. Comp. 30 (1975) 337-360.
MATHEMATICA
ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
Reap[For[max=0; p=2, p<50000, p = NextPrime[p], f = Abs[ChebyshevPsi[p]-p]; If[f > max, max = f; Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 03 2018 *)
PROG
(Perl) use ntheory ":all"; my($max, $f)=(0); forprimes { $f=abs(chebyshev_psi($_)-$_); if ($f > $max) { say; $max=$f; } } 10000; # Dana Jacobsen, Dec 29 2015
CROSSREFS
Sequence in context: A244269 A195325 A195329 * A232848 A215393 A141869
KEYWORD
nonn
AUTHOR
Michel Planat, Oct 11 2011
STATUS
approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)