A368595 Alternating sum of A006519.

-1, 1, 0, 4, 3, 5, 4, 12, 11, 13, 12, 16, 15, 17, 16, 32, 31, 33, 32, 36, 35, 37, 36, 44, 43, 45, 44, 48, 47, 49, 48, 80, 79, 81, 80, 84, 83, 85, 84, 92, 91, 93, 92, 96, 95, 97, 96, 112, 111, 113, 112, 116, 115, 117, 116, 124, 123, 125, 124, 128, 127, 129, 128

Offset: 1

Author

Jeffrey Shallit, Dec 31 2023

Keywords

• sign
• easy

Comments

a(n) <= (n/2)*log_2 n, with equality at powers of 2.

Crossrefs

Cf. A006519. A006520 (all positive signs), A136013.

Cf. A093347 (with powers of 3).

Programs

Mathematica

a[1]=-1;a[n_]:=If[OddQ[n],a[n-1]-2^IntegerExponent[n,2],a[n-1]+2^IntegerExponent[n,2]];Table[a[n],{n,63}] (* James C. McMahon, Dec 31 2023 *)

PARI

a(n) = fromdigits(Vec(Pol(binary(n))'),2) - bitand(n,1); \\ Kevin Ryde, Jan 01 2024

Python

def A368595(n): return sum(map(lambda x:(x[0]+1)*(1<Chai Wah Wu, Jan 01 2024

Formula

a(n) = Sum_{i=1..n} (-1)^i*A006519(i).

a(n) = A136013(n) - (n mod 2). - Kevin Ryde, Jan 01 2024