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Search: id:A132448
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| A132448 |
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First primitive GF(2)[X] polynomial of degree n, X^n suppressed. |
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+0
5
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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More precisely: minimum value for X=2 of GF(2)[X] polynomials P[X] such that X^n+P[X] is primitive. 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(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.
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CROSSREFS
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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.
Adjacent sequences: A132445 A132446 A132447 this_sequence A132449 A132450 A132451
Sequence in context: A096918 A075018 A125958 this_sequence A132450 A132424 A070864
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KEYWORD
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more,nonn
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AUTHOR
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Francois R. Grieu (f(AT)grieu.com), Aug 22 2007
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