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A197186
The Riemann primes of the psi type and index 2.
5
2, 17, 31, 41, 53, 101, 109, 127, 139, 179, 397, 419, 547, 787, 997, 1031, 1229, 1801, 1811, 2099, 2237, 2417, 2423, 2657, 3163, 3203, 3517, 3581, 3583, 3931, 4241, 5503, 5507, 5557, 6079, 8087, 8719, 10433, 10487, 13399, 13411, 19309, 22303, 22307, 22613
OFFSET
1,1
COMMENTS
The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |psi(p^2)-p^2|, 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.
MATHEMATICA
ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
Reap[For[max=0; p=2, p < 2000, p = NextPrime[p], f = Abs[ChebyshevPsi[p^2] - p^2]; 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 { $f=abs(chebyshev_psi($_**2)-$_**2); if ($f > $max) { say; $max=$f; } } 10000; # Dana Jacobsen, Dec 29 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Planat, Oct 11 2011
EXTENSIONS
More terms from Dana Jacobsen, Dec 29 2015
STATUS
approved