A353168 Polynomials over GF(2) that are divisible by x^2+x+1, encoded as binary numbers.

0, 7, 9, 14, 18, 21, 27, 28, 35, 36, 42, 45, 49, 54, 56, 63, 65, 70, 72, 79, 83, 84, 90, 93, 98, 101, 107, 108, 112, 119, 121, 126, 130, 133, 139, 140, 144, 151, 153, 158, 161, 166, 168, 175, 179, 180, 186, 189, 195, 196, 202, 205, 209, 214, 216, 223, 224, 231, 233

Offset: 1

Author

Jack Zhang, Apr 28 2022

Keywords

• nonn

Comments

Terms of A048727, sorted.

Crossrefs

Cf. A048727.

See also A001969 for those divisible by x + 1.

Programs

Python

from itertools import count, chain, islice
def A353168_gen(): # generator of terms
    return chain((0,),chain.from_iterable((sorted(n^ n<<1 ^ n<<2 for n in range(2**l,2**(l+1))) for l in count(0))))
A353168_list = list(islice(A353168_gen(),30)) # Chai Wah Wu, Jun 29 2022

Extensions

More terms from David A. Corneth, Apr 28 2022