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A132453 First primitive GF(2)[X] polynomial of degree n and minimal number of terms. 4
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 (list; graph; refs; listen; history; text; internal format)



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.


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

J. 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)


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.


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: A022406 A132447 A132449 * A033871 A060288 A191245

Adjacent sequences:  A132450 A132451 A132452 * A132454 A132455 A132456




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



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Last modified July 21 19:25 EDT 2019. Contains 325199 sequences. (Running on oeis4.)