

A091242


Reducible polynomials over GF(2), coded in binary.


48



4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88
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OFFSET

1,1


COMMENTS

"Coded in binary" means that a polynomial a(n)*X^n+...+a(0)*X^0 over GF(2) is represented by the binary number a(n)*2^n+...+a(0)*2^0 in Z (where a(k)=0 or 1).  M. F. Hasler, Aug 18 2014
The reducible polynomials in GF(2)[X] are the analog to the composite numbers A002808 in the integers.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
A. Karttunen, Schemeprogram for computing this sequence.
Index entries for sequences operating on GF(2)[X]polynomials


EXAMPLE

For example, 5 = 101 in binary encodes the polynomial x^2+1 which is factored as (x+1)^2 in the polynomial ring GF(2)[X].


MAPLE

filter:= proc(n) local L;
L:= convert(n, base, 2);
not Irreduc(add(L[i]*x^(i1), i=1..nops(L))) mod 2
end proc:
select(filter, [$2..200]); # Robert Israel, Aug 30 2018


CROSSREFS

Inverse: A091246. Almost complement of A014580. Union of A091209 & A091212. First differences: A091243. Characteristic function: A091247. In binary format: A091254.
Sequence in context: A284902 A023851 A285279 * A089253 A047432 A095279
Adjacent sequences: A091239 A091240 A091241 * A091243 A091244 A091245


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 03 2004


EXTENSIONS

Edited by M. F. Hasler, Aug 18 2014


STATUS

approved



