login
A295897
Numbers in whose binary expansion there are no 1-runs of odd length followed by a 0 to their right.
2
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
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
Subsequence of A004760.
Cf. A277335 (a subsequence).
Cf. A295896 (characteristic function).
Sequence in context: A325430 A104463 A072757 * A032849 A038591 A333794
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 01 2017
STATUS
approved