A284437 Number of primes between n and 2^n inclusive.

0, 1, 2, 3, 4, 9, 15, 28, 50, 93, 168, 305, 559, 1023, 1894, 3506, 6536, 12245, 22993, 43383, 82017, 155603, 295939, 564155, 1077862, 2063680, 3957800, 7603544, 14630834, 28192741, 54400018, 105097555, 203280210, 393615795, 762939100, 1480206268, 2874398504, 5586502337

Offset: 0

Author

Vincenzo Librandi, Mar 27 2017

Keywords

• nonn

Examples

			a(0) = 0 because there are 0 primes between 0 and 2^0.
a(5) = 9 because there are 9 primes between 5 and 2^5: 5, 7, 11, 13, 17, 19, 23, 29, 31 (we count the boundary of the interval in this case).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..92 (terms 0..47 from Vincenzo Librandi)

Crossrefs

Cf. A000720, A007053, A035250, A060715, A080339, A284275.

Programs

Magma

[0] cat [#PrimesInInterval(n, 2^n): n in [1..28]];

Mathematica

Join[{0}, f[n_]:=PrimePi[2^n] - PrimePi[n-1]; Array[f, 37]]

Formula

a(n) = A284275(n) + A080339(n) for n >= 1. - Amiram Eldar, Jun 11 2024