A072731 Difference of numbers of composite and prime numbers <= n.

0, -1, -2, -1, -2, -1, -2, -1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 20, 21, 20, 21, 22, 23, 24, 25, 24, 25, 24, 25, 26, 27, 28, 29, 28, 29, 30, 31, 30, 31, 30, 31, 32, 33, 34

Offset: 1

Author

Reinhard Zumkeller, Aug 08 2002

Keywords

• sign

Comments

a(n+1) = a(n) + A066247(n) - A010051(n), a(1) = 0.

a(n) < 0 iff 1 < n <= 8.

Crossrefs

Cf. A000040, A000720 (pi), A002808, A010051, A065855, A066247.

Formula

a(n) = A065855(n) - A000720(n).

a(n) = n - 2*pi(n) - 1. - Wesley Ivan Hurt, Jun 16 2013