

A132447


First primitive GF(2)[X] polynomial of degree n.


4



3, 7, 11, 19, 37, 67, 131, 285, 529, 1033, 2053, 4179, 8219, 16427, 32771, 65581, 131081, 262183, 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. Applications include maximumlength linear feedback shift registers with efficient implementation in software.


LINKS

Table of n, a(n) for n=1..31.
Index entries for sequences operating on GF(2)[X]polynomials


EXAMPLE

a(5)=37, or 100101 in binary, representing the GF(2)[X] polynomial X^5+X^2+1, because it has degree 5 and is primitive, contrary to X^5, X^5+1, X^5+x^1, X^5+X^1+1 and X^5+X^2.


CROSSREFS

a(n) is the smallest member of A091250 at least 2^n. A132448(n) = a(n)2^n, giving a more compact representation. Cf. A132449, similar with restriction to at most 5 terms. Cf. A132451, similar with restriction to exactly 5 terms. Cf. A132453, similar with restriction to minimal number of terms.
Sequence in context: A161387 A229086 A022406 * A132449 A132453 A033871
Adjacent sequences: A132444 A132445 A132446 * A132448 A132449 A132450


KEYWORD

nonn


AUTHOR

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


STATUS

approved



