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

1,1

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..13846

Index entries for sequences operating on GF(2)[X]-polynomials

Example

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.

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A246156 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE odd? A091242))))

Crossrefs

Intersection of A091242 and A005408 (odd numbers).

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

Sequence in context: A106503 A267648 A160593 * A314995 A314996 A314997

Adjacent sequences: A246153 A246154 A246155 * A246157 A246158 A246159

Keyword

base,nonn

Author

Antti Karttunen, Aug 20 2014

Status

approved