A195007 Number of primes in the range (n*sqrt(n-1), (n+1)*sqrt(n)].

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

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 07 2011

Keywords

• nonn

Examples

			a(1)=1`because 1*sqrt(1-1)<(prime 2)<=(1+1)*sqrt(1),
a(2)=1 because 2*sqrt(2-1)<(prime 3)<=(2+1)*sqrt(2).
		

Crossrefs

Cf. A006005, A192454.

Programs

Mathematica

Table[PrimePi[(n+1)*Sqrt[n]] - PrimePi[n*Sqrt[n-1]], {n, 100}] (* T. D. Noe, Sep 14 2011 *)