A293655 Numbers having in binary representation more zeros than their squares.

181, 5221, 11309, 19637, 21577, 22805, 43151, 69451, 74969, 76845, 82709, 83539, 85029, 86283, 86581, 91205, 148245, 165013, 165061, 165418, 166027, 170021, 172213, 172615, 173095, 173101, 173162, 173331, 180405, 182433, 184587, 184885, 185363, 201829, 282713

Offset: 1

Author

Alex Ratushnyak, Feb 06 2018

Keywords

• nonn
• base

Examples

			181 in base 2 is 10110101, with 3 zeros, and 181^2 is 111111111111001, with 2 zeros.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023416, A094694.

Programs

Mathematica

Select[Range[3*10^5], DigitCount[#, 2, 0] > DigitCount[#^2, 2, 0] &] (* Michael De Vlieger, Feb 21 2018 *)

PARI

nbz(n) = my(b=binary(n)); #b - hammingweight(n);
isok(n) = nbz(n) > nbz(n^2); \\ Michel Marcus, Feb 12 2018

Python

def count0(n):
    return bin(n)[2:].count('0')
for n in range(1000000):
    if count0(n*n) < count0(n):
        print(str(n), end=',')