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

1,1

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A023416, A094694.

Sequence in context: A264337 A155018 A179814 * A008379 A262141 A212938

Adjacent sequences: A293652 A293653 A293654 * A293656 A293657 A293658

Keyword

nonn,base

Author

Alex Ratushnyak, Feb 06 2018

Status

approved