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

0,12

Comments

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

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

Links

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

Formula

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

Example

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.

Prog

(JavaScript)
function bitCount(n) {
   var i, c, s;
   c=0;
   s=n.toString(2);
   for (i=0; i<s.length; i++)
      if (s.charAt(i)==1)
         c++;
   return c;
}
for (i=0; i<100; i++) document.write(bitCount(i*i)-bitCount(i)+", ");
(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
(PARI) a(n) = hammingweight(n^2) - hammingweight(n); \\ Michel Marcus, Mar 05 2023

Crossrefs

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

Sequence in context: A363857 A219558 A279210 * A034876 A091393 A359735

Adjacent sequences: A232240 A232241 A232242 * A232244 A232245 A232246

Keyword

sign,base

Author

Jon Perry, Nov 20 2013

Status

approved