A226473 a(n) is the first prime index where the gap between R(n), Riemann's prime counting function, and Pi(n), the exact prime counting function, is greater than n.

109, 556, 1327, 3296, 5380, 10343, 11767, 19202, 19361, 19371, 24121, 42863, 58243, 59453, 59473, 152959, 155809, 155863, 155893, 175594, 175618, 230393, 298545, 298557, 298974, 298986, 299277, 300072, 300135, 302547, 355093, 355111, 463171, 909917, 910219, 993762

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..36.

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

Example

RiemannR(109) = 27.4664... and PrimePi(109) = 29 give the first gap greater than 1, hence a(1) = 109.

Mathematica

Reap[For[n = 1; gap = 1, n < 10^6, n++, If[Abs[RiemannR[n] - PrimePi[n]] > gap, Print[{gap, n}]; Sow[n]; gap++]]][[2, 1]]

Crossrefs

Cf. A057794.

Sequence in context: A142640 A126856 A142915 * A142366 A103734 A232039

Adjacent sequences: A226470 A226471 A226472 * A226474 A226475 A226476

Keyword

nonn

Author

Jean-François Alcover, Sep 17 2012

Status

approved