A235033 Numbers which are factored to a different set of primes in Z as to the irreducible polynomials in GF(2)[X].

5, 9, 10, 15, 17, 18, 20, 21, 23, 25, 27, 29, 30, 33, 34, 35, 36, 39, 40, 42, 43, 45, 46, 49, 50, 51, 53, 54, 55, 57, 58, 60, 63, 65, 66, 68, 69, 70, 71, 72, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 95, 98, 99, 100, 101, 102, 105, 106

Offset

1,1

Comments

If a term is included in this sequence, then all its ordinary multiples as well as any "A048720-multiples" are included as well. (Cf. the characteristic function A235046.)

The sequence which gives all such n that A001222(n) differs from A091222(n) is a subsequence of this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences operating on (or containing) GF(2)[X]-polynomials

Example

5 is included in this sequence, because, although it is prime, its binary representation '101' encodes a polynomial x^2 + 1, which is reducible in polynomial ring GF(2)[X] as (x+1)(x+1), i.e., 5 = A048720(3,3).
9 is included in this sequence, as it factors as 3*3 in Z, the corresponding polynomial (bin.repr. '1001'): x^3 + 1 factors as (x+1)(x^2+x+1), i.e., 9 = A048720(3,7), so even although the number of prime/irreducible factors is the same, the factors themselves (i.e., their binary codes) are not exactly the same, thus 9 is included here.
On the other hand, none of 2, 3, 4, 11 and 111 are included in this sequence because they occur in the complement sequence, A235032 (please see examples there).

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A235033 (MATCHING-POS 1 0 (lambda (n) (not (or (zero? n) (equal? (ifactor n) (GF2Xfactor n)))))))

Crossrefs

Gives the positions of nonzeros in A236380, i.e., n such that A234741(n) <> A234742(n).

Characteristic function: A235046.

Complement: A235032. Subsets: A091209, A091214.

Sequence in context: A314580 A314581 A272902 * A327593 A282757 A199718

Adjacent sequences: A235030 A235031 A235032 * A235034 A235035 A235036

Keyword

nonn

Author

Antti Karttunen, Jan 02 2014

Status

approved