A132453 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..31.

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)

EXAMPLE

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.

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.

Sequence in context: A355288 A132447 A132449 * A033871 A060288 A355139

Adjacent sequences: A132450 A132451 A132452 * A132454 A132455 A132456

KEYWORD

nonn

AUTHOR

Francois R. Grieu, Aug 22 2007

STATUS

approved