A246158 Odious reducible polynomials over GF(2), coded in binary. (Polynomials with an odd number of nonzero terms that are reducible over GF(2)).

4, 8, 14, 16, 21, 22, 26, 28, 32, 35, 38, 42, 44, 49, 50, 52, 56, 62, 64, 69, 70, 74, 76, 79, 81, 82, 84, 88, 93, 94, 98, 100, 104, 107, 110, 112, 118, 121, 122, 124, 127, 128, 133, 134, 138, 140, 146, 148, 151, 152, 155, 158, 161, 162, 164, 168, 173, 174, 176, 179, 181, 182, 186, 188, 194, 196, 199, 200

Offset: 1

Author

Antti Karttunen, Aug 20 2014

Keywords

• nonn
• base

Comments

Self-inverse permutation A193231 maps each term of this sequence to some term of A246156 and vice versa.

Each term belongs into a distinct infinite cycle in permutations like A246161/A246162 and A246163/A246164 apart from 4, which is in a finite cycle (3 4) of A246161/A246162 and 4 and 8 which both are in the same (infinite) cycle of A246163/A246164.

Examples

			4, which is 100 in binary, encodes polynomial x^2, which factorizes as (x)(x) over GF(2), (4 = A048720(2,2)), thus it is reducible in that polynomial ring. It also has an odd number of nonzero terms present (equally: odd number of 1-bits in its code), in this case just one, thus 4 is a member of this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13846
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Intersection of A091242 and A000069 (odious numbers).

A238186 and A246157 are subsequences.

Cf. also A048720, A246156, A193231, A246161, A246162, A246163, A246164.