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A132451 First primitive GF(2)[X] polynomials of degree n with exactly 5 terms. 4
0, 0, 0, 0, 47, 91, 143, 285, 539, 1051, 2071, 4179, 8219, 16427, 32791, 65581, 131087, 262183, 524327, 1048659, 2097191, 4194361, 8388651, 16777243, 33554447, 67108935, 134217767, 268435539, 536870935, 1073741907, 2147483663 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

More precisely: minimum value for X=2 of primitive GF(2)[X] polynomials of degree n with exactly 5 terms, or 0 if no such polynomial exists. Applications include maximum-length linear feedback shift registers with efficient implementation in both hardware and software. Proof is needed that there exists a primitive GF(2)[X] polynomial P[X] of degree n and exactly 5 terms for all n>4.

LINKS

Table of n, a(n) for n=1..31.

Index entries for sequences operating on GF(2)[X]-polynomials

EXAMPLE

a(6)=91, or 1011011 in binary, representing the GF(2)[X] polynomial X^6+X^4+X^3+X^1+1, because it has degree 6 and exactly 5 terms and is primitive, contrary to X^6+X^3+X^2+X^1+1 and X^6+X^4+X^2+X^1+1.

CROSSREFS

For n>4, a(n) belongs to A091250. A132452(n) = a(n)-2^n, giving a more compact representation. Cf. A132447, similar with no restriction on number of terms. Cf. A132449, similar with restriction to a most 5 terms. Cf. A132453, similar with restriction to minimal number of terms.

Sequence in context: A272879 A139968 A217355 * A004943 A004963 A061153

Adjacent sequences:  A132448 A132449 A132450 * A132452 A132453 A132454

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)