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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A248020 A290435 A138227 * A364029 A301789 A244166
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Aug 20 2014
STATUS
approved

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Last modified July 15 01:36 EDT 2024. Contains 374323 sequences. (Running on oeis4.)