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A246158 Odious reducible polynomials over GF(2), coded in binary. (Polynomials with an odd number of nonzero terms that are reducible over GF(2)).

%I A246158 #15 Aug 22 2014 16:47:31
%S A246158 4,8,14,16,21,22,26,28,32,35,38,42,44,49,50,52,56,62,64,69,70,74,76,
%T A246158 79,81,82,84,88,93,94,98,100,104,107,110,112,118,121,122,124,127,128,
%U A246158 133,134,138,140,146,148,151,152,155,158,161,162,164,168,173,174,176,179,181,182,186,188,194,196,199,200
%N A246158 Odious reducible polynomials over GF(2), coded in binary. (Polynomials with an odd number of nonzero terms that are reducible over GF(2)).
%C A246158 Self-inverse permutation A193231 maps each term of this sequence to some term of A246156 and vice versa.
%C A246158 Each term belongs into a distinct infinite cycle in permutations like A246161/A246162 and A246163/A246164 apart from 4, which is in a finite cycle (3 4) of A246161/A246162 and 4 and 8 which both are in the same (infinite) cycle of A246163/A246164.
%H A246158 Antti Karttunen, <a href="/A246158/b246158.txt">Table of n, a(n) for n = 1..13846</a>
%H A246158 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e A246158 4, which is 100 in binary, encodes polynomial x^2, which factorizes as (x)(x) over GF(2), (4 = A048720(2,2)), thus it is reducible in that polynomial ring. It also has an odd number of nonzero terms present (equally: odd number of 1-bits in its code), in this case just one, thus 4 is a member of this sequence.
%o A246158 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A246158 (define A246158 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE (lambda (n) (= 1 (A010060 n))) A091242))))
%Y A246158 Intersection of A091242 and A000069 (odious numbers).
%Y A246158 A238186 and A246157 are subsequences.
%Y A246158 Cf. also A048720, A246156, A193231, A246161, A246162, A246163, A246164.
%K A246158 nonn,base
%O A246158 1,1
%A A246158 _Antti Karttunen_, Aug 20 2014