A383259 a(n) is the excess of even composites over odd composites in the first n positive integers.

0, 0, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 6, 7, 7, 8, 7, 8, 7, 8, 8, 9, 9, 10, 9, 10, 9, 10, 10, 11, 10, 11, 11, 12, 12, 13, 12, 13, 13, 14, 13, 14, 13, 14, 14, 15, 14, 15, 14, 15, 15, 16, 16, 17, 16, 17, 16, 17, 17, 18, 17, 18, 18, 19, 19, 20

Offset: 1

Author

Felix Huber, Apr 24 2025

Keywords

• nonn
• easy

Examples

			Of the first 9 positive integers are three (4, 6, 8) even and one (9) is odd, so a(9) = 3 - 1 = 2.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Composite Number

Crossrefs

Cf. A000034, A000720, A002808, A066247, A071904, A383037.

Programs

Maple

A383259:=n->`if`(n=1,0,NumberTheory:-pi(n)-(n mod 2)-1);seq(A383259(n),n=1..74);

Mathematica

a[1]:=0; a[n_]:=PrimePi[n]- Mod[n,2] - 1; Array[a,74] (* Stefano Spezia, Apr 25 2025 *)

Formula

a(n) = pi(n) - (n mod 2) - 1 = A000720(n) - A000034(n) for n > 1.

abs(a(n)-a(n-1)) = A066247(n).