A359794 Union of odd numbers and numbers with an odd 2-adic valuation.

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 93, 94

Offset: 1

Author

Antti Karttunen, Jan 25 2023

Keywords

• nonn

Comments

Numbers not of the form (2*m - 1)*4^k where m >= 1, k >= 1.

Numbers k for which the parities of k and A048675(k) differ.

The asymptotic density of this sequence is 5/6. - Amiram Eldar, Jan 25 2023

Crossrefs

Union of A005408 and A036554.

Complement of A108269.

Cf. A048675, A359832 (characteristic function).

Programs

Mathematica

Select[Range[100], OddQ[#] || OddQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 25 2023 *)

PARI

isA359794(n) = A359832(n);

Python

def A359794(n):
    def f(x):
        c, s = n+(x>>1), bin(x)[2:]
        l = len(s)
        for i in range(l&1,l,2):
            c -= int(s[i])+int('0'+s[:i],2)
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jan 29 2025