A232243 a(n) = wt(n^2) - wt(n), where wt(n) = A000120(n) is the binary weight function.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 1, 1, 2, 1, 3, 2, -1, 0, 2, 1, 2, 0, 1, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 2, 3, 3, 2, 4, -1, -1, 0, 2, 2, 1, 1, 4, 2, 2, 0, 2, 1, 2, 0, 1, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 3, 3, 5, 2, 3, 3, 0, 1, 3, 2, 4, 3, 3, 3, 2, 2, 5, 4, 0, -1, 1, -1, -1, 0, 2, 2, 2

Offset: 0

Author

Jon Perry, Nov 20 2013

Keywords

• sign
• base

Comments

A077436 lists n for which a(n) = 0.

A094694 lists n for which a(n) < 0.

Examples

			a(5): 5 = 101_2, 25 = 11001_2, so a(5) = 3 - 2 = 1.
a(23): 23 = 10111_2, 529 = 10001001_2, so a(23) = 3 - 4 = -1.
		

Links

• Dumitru Damian, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A159918, A077436, A094694, A231898.

Programs

JavaScript

function bitCount(n) {
   var i,c,s;
   c=0;
   s=n.toString(2);
   for (i=0;i
				

PARI

a(n) = hammingweight(n^2) - hammingweight(n); \\ Michel Marcus, Mar 05 2023

Python

def A232243(n): return (n**2).bit_count()-n.bit_count()
print(list(A232243(n) for n in range(10**2)))  # Dumitru Damian, Mar 04 2023

Formula

a(n) = A159918(n) - A000120(n).