A232245 Sum of the number of ones in binary representation of n and n^2.

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

Offset

0,2

Comments

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).

Links

Table of n, a(n) for n=0..81.

Formula

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

Example

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

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)+", ");

Crossrefs

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

Sequence in context: A294097 A233520 A243271 * A121895 A139555 A241814

Adjacent sequences: A232242 A232243 A232244 * A232246 A232247 A232248

Keyword

nonn,base

Author

Jon Perry, Nov 20 2013

Status

approved