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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.

%I A246157 #16 Aug 22 2014 16:47:20
%S A246157 21,35,49,69,79,81,93,107,121,127,133,151,155,161,173,179,181,199,205,
%T A246157 217,223,227,233,251,259,261,265,271,273,279,289,295,307,309,321,327,
%U A246157 331,339,341,345,367,381,385,403,405,409,421,431,439,443,453,457,465,475,481,491,493,511
%N 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.
%C A246157 Numbers n such that (A000035(n) * A010060(n) * A091247(n)) = 1.
%C A246157 This sequence is closed with respect to the self-inverse permutation A193231, meaning that A193231(a(n)) is always either the same or some other term of this sequence.
%H A246157 Antti Karttunen, <a href="/A246157/b246157.txt">Table of n, a(n) for n = 1..11665</a>
%H A246157 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e A246157 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.
%e A246157 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 1-bits (nonzero terms) present. Thus, 35 is included in this sequence.
%o A246157 (Scheme, with _Antti Karttunen_'s IntSeq-library, two alternative versions)
%o A246157 (define A246157 (COMPOSE A091242 (MATCHING-POS 1 1 (COMPOSE (lambda (n) (and (odd? n) (= 1 (A010060 n)))) A091242))))
%o A246157 (define A246157 (MATCHING-POS 1 1 (lambda (n) (= 1 (* (A000035 n) (A010060 n) (A091247 n))))))
%Y A246157 Intersection of A246156 and A246158.
%Y A246157 Intersection of A091242 and A092246.
%Y A246157 Cf. A000035, A010060, A091247, A048720, A193231.
%K A246157 nonn,base
%O A246157 1,1
%A A246157 _Antti Karttunen_, Aug 20 2014