A246158 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

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

EXAMPLE

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.

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A246158 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE (lambda (n) (= 1 (A010060 n))) A091242))))

CROSSREFS

Intersection of A091242 and A000069 (odious numbers).

A238186 and A246157 are subsequences.

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

Sequence in context: A312256 A229937 A125495 * A312257 A312258 A312259

Adjacent sequences: A246155 A246156 A246157 * A246159 A246160 A246161

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 20 2014

STATUS

approved