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

1,6

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Composite Number

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A384426 A282630 A108309 * A341307 A103469 A337932

Adjacent sequences: A383256 A383257 A383258 * A383260 A383261 A383262

Keyword

nonn,easy

Author

Felix Huber, Apr 24 2025

Status

approved