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

Author

Jean-François Alcover, Sep 17 2012

Keywords

• nonn

Examples

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

References

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

Links

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

Crossrefs

Cf. A057794.

Programs

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]]