cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A293655 #24 Mar 03 2024 10:16:19
%S A293655 181,5221,11309,19637,21577,22805,43151,69451,74969,76845,82709,83539,
%T A293655 85029,86283,86581,91205,148245,165013,165061,165418,166027,170021,
%U A293655 172213,172615,173095,173101,173162,173331,180405,182433,184587,184885,185363,201829,282713
%N A293655 Numbers having in binary representation more zeros than their squares.
%H A293655 Chai Wah Wu, <a href="/A293655/b293655.txt">Table of n, a(n) for n = 1..10000</a>
%e A293655 181 in base 2 is 10110101, with 3 zeros, and 181^2 is 111111111111001, with 2 zeros.
%t A293655 Select[Range[3*10^5], DigitCount[#, 2, 0] > DigitCount[#^2, 2, 0] &] (* _Michael De Vlieger_, Feb 21 2018 *)
%o A293655 (Python)
%o A293655 def count0(n):
%o A293655     return bin(n)[2:].count('0')
%o A293655 for n in range(1000000):
%o A293655     if count0(n*n) < count0(n):
%o A293655         print(str(n), end=',')
%o A293655 (PARI) nbz(n) = my(b=binary(n)); #b - hammingweight(n);
%o A293655 isok(n) = nbz(n) > nbz(n^2); \\ _Michel Marcus_, Feb 12 2018
%Y A293655 Cf. A023416, A094694.
%K A293655 nonn,base
%O A293655 1,1
%A A293655 _Alex Ratushnyak_, Feb 06 2018