A295897 Numbers in whose binary expansion there are no 1-runs of odd length followed by a 0 to their right.

0, 1, 3, 6, 7, 12, 13, 15, 24, 25, 27, 30, 31, 48, 49, 51, 54, 55, 60, 61, 63, 96, 97, 99, 102, 103, 108, 109, 111, 120, 121, 123, 126, 127, 192, 193, 195, 198, 199, 204, 205, 207, 216, 217, 219, 222, 223, 240, 241, 243, 246, 247, 252, 253, 255, 384, 385, 387, 390, 391, 396, 397, 399, 408, 409, 411, 414, 415, 432

Offset

1,3

Comments

No runs of 1-bits of odd length allowed in the binary expansion of n (A007088), except that when n is an odd number, then the rightmost run may have an odd length. Subsequence A277335 does not allow that exception.

A005940(1+a(n)) yields a permutation of A028982, squares and twice squares.

Running maximum without repetition of the decimal equivalent of Gray code for n (A003188). - Frédéric Nouvier, Aug 14 2020

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Formula

a(n) = A003714(n-1) XOR ( A003714(n-1) >> 1 ). - Frédéric Nouvier, Aug 14 2020

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A295897 (NONZERO-POS 1 0 A295896))
(Rust)
fn main() {
    for i in (0..2048)
        // Filter to get A003714
        .filter(|n| n & (n << 1) == 0)
        // Map to produce A295897
        .map(|n| n ^ (n >> 1))
    {
        println!("{}", i);
    }
} // Frédéric Nouvier, Aug 14 2020
(Python)
[x ^ (x>>1) for x in range(0, 2048) if (x & (x<<1) == 0)]
# Frédéric Nouvier, Aug 14 2020

Crossrefs

Cf. A005940, A028982, A280873.

Subsequence of A004760.

Cf. A277335 (a subsequence).

Cf. A295896 (characteristic function).

Sequence in context: A325430 A104463 A072757 * A032849 A038591 A333794

Adjacent sequences: A295894 A295895 A295896 * A295898 A295899 A295900

Keyword

nonn,base

Author

Antti Karttunen, Dec 01 2017

Status

approved