A182095 Number of composite numbers between 2^n and 2^(n+1).

0, 0, 1, 5, 10, 24, 50, 104, 212, 436, 886, 1792, 3631, 7319, 14771, 29737, 59826, 120322, 241753, 485652, 974989, 1956815, 3926087, 7874899, 15791397, 31660311, 63463119, 127190437, 254873548, 510663633, 1023044286, 2049300991, 4104631710, 8220611286

Offset: 0

Author

Antoine Gold, Apr 11 2012

Keywords

• nonn

Comments

Note that here, the endpoints of the interval are not counted. - Michel Marcus, Sep 05 2013

Examples

			Between 2^3 and 2^4 there are 5 composite integers: 9, 10, 12, 14, and 15.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..91 (terms 0..45 from G. C. Greubel)

Crossrefs

Cf. A036378 (number of primes between 2^n and 2^(n+1)), A075084.

Programs

Magma

[0] cat [2^n-(#PrimesUpTo(2^(n+1))-#PrimesUpTo(2^n))-1: n in [1..28]]; // Vincenzo Librandi, Aug 21 2017

Mathematica

Join[{0}, Table[2^n - (PrimePi[2^(n + 1)] - PrimePi[2^n]) - 1, {n, 33}]] (* T. D. Noe, Apr 11 2012 *)

Formula

a(n) = 2^n - 1 - A036378(n) for n >= 1. - T. D. Noe, Apr 11 2012

a(n) = A075084(2^n) - 2, for n>0. - Michel Marcus, Sep 05 2013