

A275235


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


1



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
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OFFSET

1,9


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


FORMULA

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


MATHEMATICA

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


PROG

(PARI) a(n) = primepi(n+log(n)^2)  primepi(n) \\ Felix FrÃ¶hlich, Jul 21 2016


CROSSREFS

Cf. A000040.
Sequence in context: A309121 A305871 A089049 * A029420 A194822 A029405
Adjacent sequences: A275232 A275233 A275234 * A275236 A275237 A275238


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 21 2016


STATUS

approved



