A132453 First primitive GF(2)[X] polynomial of degree n and minimal number of terms.

3, 7, 11, 19, 37, 67, 131, 285, 529, 1033, 2053, 4179, 8219, 16427, 32771, 65581, 131081, 262273, 524327, 1048585, 2097157, 4194307, 8388641, 16777243, 33554441, 67108935, 134217767, 268435465, 536870917, 1073741907, 2147483657

Offset: 1

Author

Francois R. Grieu, Aug 22 2007

Keywords

• nonn

Comments

More precisely: minimum value for X=2 of primitive GF(2)[X] polynomials of degree n and minimal number of terms for such polynomials. Applications include maximum-length linear feedback shift registers with efficient implementation in both hardware and software.

Examples

			a(10)=1033, or 10000001001 in binary, representing the GF(2)[X] polynomial X^10+X^3+1, because this polynomial has degree 10, it has 3 terms and no degree 10 polynomial with less terms than that is primitive and it is primitive, contrary to X^10+X^1+1, X^10+X^2+1 and X^10+X^2+X^1.
		

Links

• Joerg Arndt, Polynomials as lists of coefficients for 2<=n<=400
• Index entries for sequences operating on GF(2)[X]-polynomials
• Index entries for sequences related to trinomials over GF(2)

Crossrefs

Subset of A091250. A132454(n) encodes a(n) in a more compact representation. Cf. A132447, similar, with no restriction on number of terms. Cf. A132449, similar, with restriction to at most 5 terms. Cf. A132451, similar, with restriction to exactly 5 terms.