A216709 a(n) is the integer closest to Riemann's prime counting function R(n*10^6) minus the prime counting function pi(n*10^6).

29, -9, 0, 33, -64, 24, -38, -6, -53, 88, -3, -46, -51, 25, 34, 1, -18, -117, -46, -36, 18, -77, 27, 39, 3, 33, -6, 2, 7, -41, -139, -61, -104, -108, 106, 135, 198, 190, 3, -84, -102, 38, 50, 52, 55, -131, -134, -16, 99, -67, -53, -90, -49, -9, 127, 72, -13, 50, -17, 39, -85, 114

Offset

1,1

Comments

H. M. Edwards gives a(1)=30 instead of 29; he may have considered 1 a prime.

References

H. M. Edwards, Riemann's Zeta Function, Dover Publications, New York, 1974 (ISBN 978-0-486-41740-0), page 35.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Riemann Prime Counting Function.

Mathematica

Table[ Round[ RiemannR[n*10^6] - PrimePi[n*10^6]], {n, 1, 40}]

Crossrefs

Cf. A057794.

Sequence in context: A040819 A128370 A040818 * A040817 A309007 A070714

Adjacent sequences: A216706 A216707 A216708 * A216710 A216711 A216712

Keyword

sign

Author

Jean-François Alcover, Sep 17 2012

Extensions

Corrected and extended by Vincenzo Librandi, Jul 19 2013

Status

approved