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Search: id:A132447
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| A132447 |
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First primitive GF(2)[X] polynomial of degree n. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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More precisely: Minimum value for X=2 of primitive GF(2)[X] polynomials of degree n. Applications include maxmimum-length linear feedback shift registers with efficient implementation in software.
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LINKS
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Index entries for sequences operating on GF(2)[X]-polynomials
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EXAMPLE
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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.
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CROSSREFS
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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: A092102 A123080 A022406 this_sequence A132449 A132453 A060288
Adjacent sequences: A132444 A132445 A132446 this_sequence A132448 A132449 A132450
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KEYWORD
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nonn
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AUTHOR
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Francois R. Grieu (f(AT)grieu.com), Aug 22 2007
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