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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 (list; graph; refs; listen; history; text; internal format)
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, Scheme-program 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^(i-1), 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

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)