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

%I A383259 #13 Apr 25 2025 20:38:05
%S A383259 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,
%T A383259 10,9,10,10,11,10,11,11,12,12,13,12,13,13,14,13,14,13,14,14,15,14,15,
%U A383259 14,15,15,16,16,17,16,17,16,17,17,18,17,18,18,19,19,20
%N A383259 a(n) is the excess of even composites over odd composites in the first n positive integers.
%H A383259 Felix Huber, <a href="/A383259/b383259.txt">Table of n, a(n) for n = 1..10000</a>
%H A383259 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompositeNumber.html">Composite Number</a>
%F A383259 a(n) = pi(n) - (n mod 2) - 1 = A000720(n) - A000034(n) for n > 1.
%F A383259 abs(a(n)-a(n-1)) = A066247(n).
%e A383259 Of the first 9 positive integers are three (4, 6, 8) even and one (9) is odd, so a(9) = 3 - 1 = 2.
%p A383259 A383259:=n->`if`(n=1,0,NumberTheory:-pi(n)-(n mod 2)-1);seq(A383259(n),n=1..74);
%t A383259 a[1]:=0; a[n_]:=PrimePi[n]- Mod[n,2] - 1; Array[a,74] (* _Stefano Spezia_, Apr 25 2025 *)
%Y A383259 Cf. A000034, A000720, A002808, A066247, A071904, A383037.
%K A383259 nonn,easy
%O A383259 1,6
%A A383259 _Felix Huber_, Apr 24 2025