login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..39.

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

Cf. A196669, A197185, A197186, A197188.

Sequence in context: A249644 A103144 A105909 * A086498 A211655 A055387

Adjacent sequences:  A197184 A197185 A197186 * A197188 A197189 A197190

KEYWORD

nonn,more

AUTHOR

Michel Planat, Oct 11 2011

EXTENSIONS

More terms from Dana Jacobsen, Dec 28 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)