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

1,2

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A023416, A030130, A164874.

Sequence in context: A232779 A086986 A346126 * A057811 A284489 A026343

Adjacent sequences: A384186 A384187 A384188 * A384190 A384191 A384192

Keyword

nonn,base

Author

Chai Wah Wu, May 21 2025

Status

approved