A232243 - OEIS

%I #18 Mar 05 2023 01:57:32

%S 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,

%T 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,

%U 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

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

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

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

%H Dumitru Damian, <a href="/A232243/b232243.txt">Table of n, a(n) for n = 0..10000</a>

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

%e a(5): 5 = 101_2, 25 = 11001_2, so a(5) = 3 - 2 = 1.

%e a(23): 23 = 10111_2, 529 = 10001001_2, so a(23) = 3 - 4 = -1.

%o (JavaScript)

%o function bitCount(n) {

%o    var i,c,s;

%o    c=0;

%o    s=n.toString(2);

%o    for (i=0;i<s.length;i++)

%o       if (s.charAt(i)==1)

%o          c++;

%o    return c;

%o }

%o for (i=0;i<100;i++) document.write(bitCount(i*i)-bitCount(i)+", ");

%o (Python)

%o def A232243(n): return (n**2).bit_count()-n.bit_count()

%o print(list(A232243(n) for n in range(10**2)))  # _Dumitru Damian_, Mar 04 2023

%o (PARI) a(n) = hammingweight(n^2) - hammingweight(n); \\ _Michel Marcus_, Mar 05 2023

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

%K sign,base

%O 0,12

%A _Jon Perry_, Nov 20 2013