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
Dana Jacobsen, Table of n, a(n) for n = 1..583
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
KEYWORD
nonn
AUTHOR
Michel Planat, Oct 11 2011
STATUS
approved