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A384189 Numbers whose number of zeros in their binary representation is not equal to 1.

%I A384189 #14 May 22 2025 05:23:06
%S A384189 1,3,4,7,8,9,10,12,15,16,17,18,19,20,21,22,24,25,26,28,31,32,33,34,35,
%T A384189 36,37,38,39,40,41,42,43,44,45,46,48,49,50,51,52,53,54,56,57,58,60,63,
%U A384189 64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82
%N A384189 Numbers whose number of zeros in their binary representation is not equal to 1.
%C A384189 Numbers m such that A023416(m) != 1. Complement of A030130.
%H A384189 Paolo Xausa, <a href="/A384189/b384189.txt">Table of n, a(n) for n = 1..10000</a>
%e A384189 15 is a term since its binary representation 1111 has no zeros.
%e A384189 53 is a term since its binary representation 110101 has two zeros.
%t A384189 Select[Range[100], DigitCount[#, 2, 0] != 1 &] (* _Paolo Xausa_, May 22 2025 *)
%o A384189 (Python)
%o A384189 def A384189(n):
%o A384189     def f(x):
%o A384189         l, s = x.bit_length(), bin(x)[2:]
%o A384189         if (m:=s.count('0'))>0: return n+s.find('0')+((m>1)^1)+(l*(l-3)>>1)
%o A384189         return n+(l*(l-1)>>1)
%o A384189     m, k = n, f(n)
%o A384189     while m != k: m, k = k, f(k)
%o A384189     return m
%Y A384189 Cf. A023416, A030130, A164874.
%K A384189 nonn,base
%O A384189 1,2
%A A384189 _Chai Wah Wu_, May 21 2025