1,1

More precisely: minimum value for X=2 of primitive GF(2)[X] polynomials of degree n with at most 5 terms. Applications include maxmimum-length linear feedback shift registers with efficient implementation in both hardware and software. The limitation to 5 terms occurs first for a(32), which is 4294967493 representing X^32+X^7+X^6+X^2+1, rather than 4294967471 representing X^32+X^7+X^5+X^3+X^2+X^1+1. Proof is needed that there exists a primitive GF(2)[X] polynomial P[X] of degree n and at most 5 terms for all positive n.

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

a(5)=37, or 100101 in binary, representing the GF(2)[X] polynomial X^5+X^2+1, because it has degree 5 and no more than 5 terms and is primitive, contrary to X^5, X^5+1, X^5+X^1, X^5+X^1+1 and X^5+X^2.

Subset of A091250. A132450(n) = a(n)-2^n, giving a more compact representation. Cf. A132447, similar with no restriction on number of terms. Cf. A132451, similar with restriction to exactly 5 terms. Cf. A132453, similar with restriction to minimal number of terms.

Sequence in context: A161387 A022406 A132447 this_sequence A132453 A060288 A111056

Adjacent sequences: A132446 A132447 A132448 this_sequence A132450 A132451 A132452

nonn

Francois R. Grieu (f(AT)grieu.com), Aug 22 2007