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

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, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 60, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset: 1

Author

Chai Wah Wu, May 21 2025

Keywords

• nonn
• base

Comments

Numbers m such that A023416(m) != 1. Complement of A030130.

Examples

			15 is a term since its binary representation 1111 has no zeros.
53 is a term since its binary representation 110101 has two zeros.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023416, A030130, A164874.

Programs

Mathematica

Select[Range[100], DigitCount[#, 2, 0] != 1 &] (* Paolo Xausa, May 22 2025 *)

Python

def A384189(n):
    def f(x):
        l, s = x.bit_length(), bin(x)[2:]
        if (m:=s.count('0'))>0: return n+s.find('0')+((m>1)^1)+(l*(l-3)>>1)
        return n+(l*(l-1)>>1)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m