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A132448 First primitive GF(2)[X] polynomial of degree n, X^n suppressed. 4
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, 175, 83, 231, 5, 119, 63 (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] such that X^n+P[X] is primitive. Applications include maximum-length linear feedback shift registers with efficient implementation in software.

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 is primitive, contrary to X^11, X^11+1, X^11+X^1, X^11+X^1+1 and X^11+X^2.

CROSSREFS

2^n+a(n) is the smallest member of A091250 at least 2^n. A132447(n) = a(n)+2^n and gives the corresponding primitive polynomial. Cf. A132450, similar with restriction to at most 5 terms. Cf. A132452, similar with restriction to exactly 5 terms. Cf. A132454, similar with restriction to minimal number of terms.

Sequence in context: A324974 A125958 A247244 * A132450 A132424 A070864

Adjacent sequences:  A132445 A132446 A132447 * A132449 A132450 A132451

KEYWORD

more,nonn

AUTHOR

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

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)