A246156 Odd reducible polynomials over GF(2), coded in binary. (Polynomials with the constant term 1 that are reducible over GF(2)).

5, 9, 15, 17, 21, 23, 27, 29, 33, 35, 39, 43, 45, 49, 51, 53, 57, 63, 65, 69, 71, 75, 77, 79, 81, 83, 85, 89, 93, 95, 99, 101, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 133, 135, 139, 141, 147, 149, 151, 153, 155, 159, 161, 163, 165, 169, 173, 175, 177, 179, 181, 183, 187, 189, 195, 197, 199, 201

Offset: 1

Author

Antti Karttunen, Aug 20 2014

Keywords

• base
• nonn

Comments

Self-inverse permutation A193231 maps each term of this sequence to some term of A246158 and vice versa.

Examples

			5, which is 101 in binary, encodes polynomial x^2 + 1, which factorizes as (x+1)(x+1) over GF(2), (5 = A048720(3,3)), thus it is reducible in that polynomial ring. Also, its constant term is 1, (not zero), thus 5 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 A005408 (odd numbers).

A246157 is a subsequence. Cf. also A048720, A193231, A246158.

Programs

Maple

filter:= proc(n) local L,p,x;
    L:= convert(n,base,2);
    p:= add(L[i]*x^(i-1),i=1..nops(L));
    not (Irreduc(p) mod 2)
end proc:
select(filter,[seq(2*i+1,i=1..100)]); # Robert Israel, Aug 21 2014