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A132450 First primitive GF(2)[X] polynomials of degree n with at most 5 terms, X^n suppressed. 5
1, 3, 3, 3, 5, 3, 3, 29, 17, 9, 5, 83, 27, 43, 3, 45, 9, 39, 39, 9, 5, 3, 33, 27, 9, 71, 39, 9, 5, 83, 9, 197, 83, 281, 5, 387, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

More precisely: minimum value for X=2 of GF(2)[X] polynomials P[X] with at most 4 terms such that X^n+P[X] is primitive. Applications include maximum-length linear feedback shift registers with efficient implementation in both hardware and software. The limitation of the number of terms occurs first for a(32), which is 197 representing X^7+X^6+X^2+1, rather than 175 representing 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.

LINKS

Table of n, a(n) for n=1..37.

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

EXAMPLE

a(11)=5, or 101 in binary, representing the GF(2)[X] polynomial X^2+1, because X^11+X^2+1 has no more than 5 terms and X is primitive, contrary to X^11, X^11+1, X^11+X^1, X^11+X^1+1 and X^11+X^2.

CROSSREFS

A132450 2^n+a(n) belongs to A091250. A132449(n) = a(n)+2^n and gives the corresponding primitive polynomial. Cf. A132448, similar with no restriction on number of terms. Cf. A132452, similar with restriction to exactly 5 terms.

Sequence in context: A125958 A247244 A132448 * A132424 A070864 A321790

Adjacent sequences:  A132447 A132448 A132449 * A132451 A132452 A132453

KEYWORD

more,nonn

AUTHOR

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

STATUS

approved

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Last modified October 17 22:21 EDT 2019. Contains 328134 sequences. (Running on oeis4.)