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.

1, 111, 123, 219, 411, 511, 959, 1983, 2031, 3099, 3459, 3579, 4847, 5371, 6159, 7023, 7131, 7141, 7231, 7899, 7913, 8071, 8079, 9179, 12387, 12783, 13289, 15843, 26223, 27771, 28453, 28903, 31529, 31539, 39007, 45419, 49251, 49659, 51087, 53677, 56137, 57219, 61923

Offset

0,2

Comments

These are odd nonprime numbers in A235032. After a(0)=1, the odd composite numbers in A235032.

The terms a(1) - a(42) are all semiprimes. Presumably terms with a larger number of prime factors also exist.

Links

Table of n, a(n) for n=0..42.

Example

111 = 3*37. When these two prime factors (both terms of A091206), with binary representations '11' and '100101', are multiplied as:
   100101
  1001010
  -------
  1101111 = 111 in decimal
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.
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).

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A235039 (MATCHING-POS 0 1 (lambda (n) (and (odd? n) (not (prime? n)) (equal? (ifactor n) (GF2Xfactor n))))))

Crossrefs

A subsequence of A235032, A235036, A235040 and A235045.

Sequence in context: A034840 A135643 A070798 * A279423 A213879 A095613

Adjacent sequences: A235036 A235037 A235038 * A235040 A235041 A235042

Keyword

nonn

Author

Antti Karttunen, Jan 02 2014

Status

approved