A246157 Reducible polynomials over GF(2) which are both odd and odious when coded in binary, or equally, which have an odd number of nonzero terms, with the constant term being 1.

21, 35, 49, 69, 79, 81, 93, 107, 121, 127, 133, 151, 155, 161, 173, 179, 181, 199, 205, 217, 223, 227, 233, 251, 259, 261, 265, 271, 273, 279, 289, 295, 307, 309, 321, 327, 331, 339, 341, 345, 367, 381, 385, 403, 405, 409, 421, 431, 439, 443, 453, 457, 465, 475, 481, 491, 493, 511

Offset

1,1

Comments

Numbers n such that (A000035(n) * A010060(n) * A091247(n)) = 1.

This sequence is closed with respect to the self-inverse permutation A193231, meaning that A193231(a(n)) is always either the same or some other term of this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..11665

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

Example

35 in binary is 100011, which encodes polynomial x^5 + x + 1, which factorizes as (x^2 + x + 1)(x^3 + x^2 + 1) over GF(2) (35 = A048720(7,13)), thus it is reducible in that polynomial ring.
Also, it is odd (the least significant bit is 1, that is, the constant term is not zero) and also odious, as there are three 1-bits (nonzero terms) present. Thus, 35 is included in this sequence.

Prog

(Scheme, with Antti Karttunen's IntSeq-library, two alternative versions)
(define A246157 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE (lambda (n) (and (odd? n) (= 1 (A010060 n)))) A091242))))
(define A246157 (MATCHING-POS 1 1 (lambda (n) (= 1 (* (A000035 n) (A010060 n) (A091247 n))))))

Crossrefs

Intersection of A246156 and A246158.

Intersection of A091242 and A092246.

Cf. A000035, A010060, A091247, A048720, A193231.

Sequence in context: A248020 A290435 A138227 * A364029 A301789 A244166

Adjacent sequences: A246154 A246155 A246156 * A246158 A246159 A246160

Keyword

nonn,base

Author

Antti Karttunen, Aug 20 2014

Status

approved