OFFSET
1,3
LINKS
EXAMPLE
2, 3 and 11 are included in this sequence, because they occur in A091206. That is, they are all primes, and encode irreducible polynomials in ring GF(2)[X] via their binary representations: For 2, '10' in binary, corresponds to polynomial x, and for 3, '11' in binary, corresponds to polynomial x+1, and for 11, '1011' in binary, corresponds to polynomial x^3+x+1, which are all irreducible in GF(2)[X].
4 is included in this sequence, because it factors as 2*2, but also because the corresponding GF(2)[X] polynomial x^2 factors as x*x (with the polynomial x encoded by the number 2).
5 is NOT included in this sequence, because, although it is prime, the corresponding polynomial (5 in binary is '101'): x^2 + 1 is not irreducible in GF(2)[X], but factors as (x+1)(x+1), i.e., we have 5 = A048720(3,3).
111 is included, as it is a product of two primes, 3*37, and these primes encode via their binary representations, '11' and '100101', two polynomials irreducible in GF(2)[X]: x+1 and x^5 + x^2 + 1, whose product, x^6 + x^5 + x^3 + x^2 + x + 1, is encoded by 111's binary representation, '1101111'.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A235032 (MATCHING-POS 1 0 (lambda (n) (or (zero? n) (equal? (ifactor n) (GF2Xfactor n))))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2014
STATUS
approved