A232245 - OEIS

%I #9 Nov 22 2013 14:23:21

%S 0,2,2,4,2,5,4,6,2,5,5,8,4,7,6,8,2,5,5,8,5,9,8,7,4,8,7,10,6,9,8,10,2,

%T 5,5,8,5,9,8,11,5,8,9,11,8,12,7,9,4,8,8,9,7,12,10,12,6,10,9,12,8,11,

%U 10,12,2,5,5,8,5,9,8,11,5,9,9,13,8,11,11,10,5,9

%N Sum of the number of ones in binary representation of n and n^2.

%C The sequence is never 1 or 3, but seems to take on all other values. The fact it is never 3 can be used to prove if n^2 has exactly 4 1's then it must have an even number of 0's (A231898).

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

%e 5 is 101 and 25 is 11001, so a(5) = 2 + 3 = 5.

%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++) if (s.charAt(i)==1) c++;

%o return c;

%o }

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

%Y Cf. A000120, A159918, A077436, A094694, A231898, A232243.

%K nonn,base

%O 0,2

%A _Jon Perry_, Nov 20 2013