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A246158 Odious reducible polynomials over GF(2), coded in binary. (Polynomials with an odd number of nonzero terms that are reducible over GF(2)). 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 25 09:40 EDT 2021. Contains 347654 sequences. (Running on oeis4.)