A275235 Number of primes between n and n+log(n)^2.

0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 1, 1, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 5, 5, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4

Offset: 1

Author

Clark Kimberling, Jul 21 2016

Keywords

• nonn
• easy

Comments

According to Schinzel's formulation of Cramer's conjecture, a(n) > 0 for n > 7; see Guy.

References

• R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004, page 11.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040.

Programs

Mathematica

Table[PrimePi[n + Log[n]^2] - PrimePi[n], {n, 1, 200}]

PARI

a(n) = primepi(n+log(n)^2) - primepi(n) \\ Felix Fröhlich, Jul 21 2016

Formula

a(n) ~ log(n). - Ilya Gutkovskiy, Jul 22 2016