

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 maximumlength 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



