cp's OEIS Frontend

A235039 Odd numbers which are factored to the same set of primes in Z as to the irreducible polynomials in GF(2)[X]; odd terms of A235036.

%I A235039 #18 Feb 05 2014 10:52:34
%S A235039 1,111,123,219,411,511,959,1983,2031,3099,3459,3579,4847,5371,6159,
%T A235039 7023,7131,7141,7231,7899,7913,8071,8079,9179,12387,12783,13289,15843,
%U A235039 26223,27771,28453,28903,31529,31539,39007,45419,49251,49659,51087,53677,56137,57219,61923
%N A235039 Odd numbers which are factored to the same set of primes in Z as to the irreducible polynomials in GF(2)[X]; odd terms of A235036.
%C A235039 These are odd nonprime numbers in A235032. After a(0)=1, the odd composite numbers in A235032.
%C A235039 The terms a(1) - a(42) are all semiprimes. Presumably terms with a larger number of prime factors also exist.
%e A235039 111 = 3*37. When these two prime factors (both terms of A091206), with binary representations '11' and '100101', are multiplied as:
%e A235039    100101
%e A235039   1001010
%e A235039   -------
%e A235039   1101111 = 111 in decimal
%e A235039 we see that the intermediate products 1*37 and 2*37 can be added together without producing any carry-bits (as they have no 1-bits in the same columns/bit-positions), so A048720(3,37) = 3*37 and thus 111 is included in this sequence.
%e A235039 Note that unlike in A235040, 15 = 3*5 is not included in this sequence, because its prime factor 5 is not in A091206, but instead decomposes further as A048720(3,3).
%o A235039 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A235039 (define A235039 (MATCHING-POS 0 1 (lambda (n) (and (odd? n) (not (prime? n)) (equal? (ifactor n) (GF2Xfactor n))))))
%Y A235039 A subsequence of A235032, A235036, A235040 and A235045.
%K A235039 nonn
%O A235039 0,2
%A A235039 _Antti Karttunen_, Jan 02 2014