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Numbers having in binary representation more zeros than their squares.
1

%I #24 Mar 03 2024 10:16:19

%S 181,5221,11309,19637,21577,22805,43151,69451,74969,76845,82709,83539,

%T 85029,86283,86581,91205,148245,165013,165061,165418,166027,170021,

%U 172213,172615,173095,173101,173162,173331,180405,182433,184587,184885,185363,201829,282713

%N Numbers having in binary representation more zeros than their squares.

%H Chai Wah Wu, <a href="/A293655/b293655.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[3*10^5], DigitCount[#, 2, 0] > DigitCount[#^2, 2, 0] &] (* _Michael De Vlieger_, Feb 21 2018 *)

%o (Python)

%o def count0(n):

%o return bin(n)[2:].count('0')

%o for n in range(1000000):

%o if count0(n*n) < count0(n):

%o print(str(n), end=',')

%o (PARI) nbz(n) = my(b=binary(n)); #b - hammingweight(n);

%o isok(n) = nbz(n) > nbz(n^2); \\ _Michel Marcus_, Feb 12 2018

%Y Cf. A023416, A094694.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Feb 06 2018