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A197187 The Riemann primes of the psi type and index 3. 5
2, 3, 5, 7, 11, 13, 17, 29, 59, 67, 97, 103, 149, 151, 233, 251, 277, 311, 313, 479, 643, 719, 919, 967, 1039, 1373, 1489, 1553, 1847, 1973, 1979, 2663, 2953, 3323, 3677, 3691, 4651, 4663, 4789 (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^3)-p^3|, 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 < 1000, p = NextPrime[p], f = Abs[ChebyshevPsi[p^3] - p^3]; 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 { $f=abs(chebyshev_psi($_**3)-$_**3); if ($f > $max) { say; $max=$f; } } 1000; # Dana Jacobsen, Dec 28 2015
CROSSREFS
Sequence in context: A249644 A103144 A105909 * A086498 A211655 A359138
KEYWORD
nonn,more
AUTHOR
Michel Planat, Oct 11 2011
EXTENSIONS
More terms from Dana Jacobsen, Dec 28 2015
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)