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

1,2

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

Links

Table of n, a(n) for n=1..78.

Mathematica

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

Prog

(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

Crossrefs

Union of A005408 and A036554.

Complement of A108269.

Cf. A048675, A359832 (characteristic function).

Sequence in context: A213257 A367401 A039213 * A326947 A256450 A119605

Adjacent sequences: A359791 A359792 A359793 * A359795 A359796 A359797

Keyword

nonn

Author

Antti Karttunen, Jan 25 2023

Status

approved