

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

This sequence is closed with respect to the selfinverse 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 1bits (nonzero terms) present. Thus, 35 is included in this sequence.


PROG



CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



