A094812 Number of odd composites between 2^n and 2^(n + 1).

0, 0, 0, 2, 3, 9, 19, 41, 85, 181, 375, 769, 1584, 3224, 6580, 13354, 27059, 54521, 110682, 223509, 450702, 908240, 1828936, 3680596, 7402790, 14883096, 29908688, 60081574, 120655821, 242228178, 486173375, 975559168, 1957148063, 3925643991

Offset: 0

Author

Andrew S. Plewe, Jun 11 2004

Keywords

• easy
• nonn

Comments

This sequence may be related to n-ary rooted trees of a fixed height. For instance, the first few terms of A036616 are:

1, 1, 1, 2, 4, 9, 19, 41, 86, 182, 376, 776, 1579, ...

and in A036622:

1, 1, 1, 2, 4, 9, 19, 42, 88, 188, 393, 821, 1692, ...

whereas in the present sequence we have:

0, 0, 0, 2, 3, 9, 19, 41, 85, 181, 375, 769, 1584, ...

Examples

			a(3) = 2 because in the interval 2^3..2^4 = [8..16] there are two odd composites: 9 = 3^2, 15 = 3 * 5.
		

Crossrefs

Cf. A036616, A036622, A071904.

Programs

Mathematica

f[n_] := (2^(n - 1) - PrimePi[2^(n + 1)] + PrimePi[2^n]); Table[ f[n], {n, 32}] (* Robert G. Wilson v, Jun 15 2004 *)

Formula

Members of A071904 that lie between 2^n and 2^(n + 1).

Extensions

More terms from Robert G. Wilson v, Jun 15 2004