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