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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

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

Cf. A196667, A197186, A197187, A197188.

Sequence in context: A244269 A195325 A195329 * A232848 A215393 A141869

Adjacent sequences:  A197182 A197183 A197184 * A197186 A197187 A197188

KEYWORD

nonn

AUTHOR

Michel Planat, Oct 11 2011

STATUS

approved

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Last modified July 9 14:56 EDT 2020. Contains 335543 sequences. (Running on oeis4.)