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%I #8 May 06 2022 13:13:51
%S 0,0,0,0,47,91,143,285,539,1051,2071,4179,8219,16427,32791,65581,
%T 131087,262183,524327,1048659,2097191,4194361,8388651,16777243,
%U 33554447,67108935,134217767,268435539,536870935,1073741907,2147483663
%N First primitive GF(2)[X] polynomials of degree n with exactly 5 terms.
%C 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.
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e 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.
%Y 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.
%K nonn
%O 1,5
%A Francois R. Grieu (f(AT)grieu.com), Aug 22 2007
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