A210518 Number of primes up to 10^(n/4).

0, 0, 2, 3, 4, 7, 11, 16, 25, 40, 65, 102, 168, 275, 446, 739, 1229, 2039, 3401, 5703, 9592, 16144, 27293, 46243, 78498, 133551, 227647, 388683, 664579, 1138288, 1951957, 3351550, 5761455, 9915892, 17082666, 29458442, 50847534, 87842213, 151876932, 262795354

Offset: 0

Author

Vladimir Pletser, Jan 26 2013

Keywords

• nonn
• hard

Examples

			a(1) = 0 because 10^(1/4) = 1.77828... and there are no primes less than that.
a(2) = 2 because sqrt(10) = 3.16228... and there are 2 primes below that.
a(3) = 3 because 10^(3/4) = 5.62341... and there are 3 primes below that.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..80 (calculated using Kim Walisch's primecount)
• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf. A000720, A006880, A018072.

Programs

Mathematica

Table[PrimePi[10^(n/4)], {n, 0, 39}] (* Alonso del Arte, Jan 26 2013 *)

Formula

a(n) = primepi(10^(n/4)) = A000720(A018072(n)).