A246156 - OEIS

%I #17 Aug 22 2014 16:47:10

%S 5,9,15,17,21,23,27,29,33,35,39,43,45,49,51,53,57,63,65,69,71,75,77,

%T 79,81,83,85,89,93,95,99,101,105,107,111,113,119,121,123,125,127,129,

%U 133,135,139,141,147,149,151,153,155,159,161,163,165,169,173,175,177,179,181,183,187,189,195,197,199,201

%N Odd reducible polynomials over GF(2), coded in binary. (Polynomials with the constant term 1 that are reducible over GF(2)).

%C Self-inverse permutation A193231 maps each term of this sequence to some term of A246158 and vice versa.

%H Antti Karttunen, <a href="/A246156/b246156.txt">Table of n, a(n) for n = 1..13846</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

%e 5, which is 101 in binary, encodes polynomial x^2 + 1, which factorizes as (x+1)(x+1) over GF(2), (5 = A048720(3,3)), thus it is reducible in that polynomial ring. Also, its constant term is 1, (not zero), thus 5 is a member of this sequence.

%p filter:= proc(n) local L,p,x;

%p     L:= convert(n,base,2);

%p     p:= add(L[i]*x^(i-1),i=1..nops(L));

%p     not (Irreduc(p) mod 2)

%p end proc:

%p select(filter,[seq(2*i+1,i=1..100)]); # _Robert Israel_, Aug 21 2014

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A246156 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE odd? A091242))))

%Y Intersection of A091242 and A005408 (odd numbers).

%Y A246157 is a subsequence. Cf. also A048720, A193231, A246158.

%K base,nonn

%O 1,1

%A _Antti Karttunen_, Aug 20 2014