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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

MathWorld entry, Riemann's 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-Fran├žois Alcover, Sep 17 2012

STATUS

approved

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Last modified January 17 19:53 EST 2022. Contains 350406 sequences. (Running on oeis4.)