A395963 Numbers k such that A395961(k) = 1.

1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 92, 94, 97, 99, 101, 103, 105, 107, 109, 111, 112, 114, 116, 118

Offset

1,2

Comments

Complement of A395962.

Links

Table of n, a(n) for n=1..60.

Benoit Cloitre, The Thue-Morse Transform, arXiv:2604.06243 [math.NT], 2026.

Formula

a(n) = 2*(n-1) + 1 - A395961(2*(n-1)) for n >= 1.

Prog

(Python)
def A395961(n):
    s, p = 0, 0
    while (1 << p) <= n:
        if (p & 3) == 0:
            s ^= (n >> p) & 1
        p += 1
    return s
print([k for k in range(120) if A395961(k) == 1])

Crossrefs

Cf. A000035, A000069, A001969, A010060, A158704, A158705, A341389, A395958, A395959, A395960, A395961, A395962, A395964, A395965, A395966.

Sequence in context: A329831 A329938 A247429 * A187232 A187907 A024806

Adjacent sequences: A395960 A395961 A395962 * A395964 A395965 A395966

Keyword

nonn,base,easy

Author

Benoit Cloitre, May 12 2026

Status

approved