A246157 Reducible polynomials over GF(2) which are both odd and odious when coded in binary, or equally, which have an odd number of nonzero terms, with the constant term being 1.

21, 35, 49, 69, 79, 81, 93, 107, 121, 127, 133, 151, 155, 161, 173, 179, 181, 199, 205, 217, 223, 227, 233, 251, 259, 261, 265, 271, 273, 279, 289, 295, 307, 309, 321, 327, 331, 339, 341, 345, 367, 381, 385, 403, 405, 409, 421, 431, 439, 443, 453, 457, 465, 475, 481, 491, 493, 511

Offset: 1

Author

Antti Karttunen, Aug 20 2014

Keywords

• nonn
• base

Comments

Numbers n such that (A000035(n) * A010060(n) * A091247(n)) = 1.

This sequence is closed with respect to the self-inverse permutation A193231, meaning that A193231(a(n)) is always either the same or some other term of this sequence.

Examples

			35 in binary is 100011, which encodes polynomial x^5 + x + 1, which factorizes as (x^2 + x + 1)(x^3 + x^2 + 1) over GF(2) (35 = A048720(7,13)), thus it is reducible in that polynomial ring.
Also, it is odd (the least significant bit is 1, that is, the constant term is not zero) and also odious, as there are three 1-bits (nonzero terms) present. Thus, 35 is included in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11665
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Intersection of A246156 and A246158.

Intersection of A091242 and A092246.

Cf. A000035, A010060, A091247, A048720, A193231.