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%I #11 May 06 2022 13:13:51
%S 3,7,11,19,37,67,131,285,529,1033,2053,4179,8219,16427,32771,65581,
%T 131081,262183,524327,1048585,2097157,4194307,8388641,16777243,
%U 33554441,67108935,134217767,268435465,536870917,1073741907,2147483657
%N First primitive GF(2)[X] polynomial of degree n with at most 5 terms.
%C More precisely: minimum value for X=2 of primitive GF(2)[X] polynomials of degree n with at most 5 terms. Applications include maximum-length linear feedback shift registers with efficient implementation in both hardware and software. The limitation to 5 terms occurs first for a(32), which is 4294967493 representing X^32+X^7+X^6+X^2+1, rather than 4294967471 representing X^32+X^7+X^5+X^3+X^2+X^1+1. Proof is needed that there exists a primitive GF(2)[X] polynomial P[X] of degree n and at most 5 terms for all positive n.
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e a(5)=37, or 100101 in binary, representing the GF(2)[X] polynomial X^5+X^2+1, because it has degree 5 and no more than 5 terms and is primitive, contrary to X^5, X^5+1, X^5+X^1, X^5+X^1+1 and X^5+X^2.
%Y Subset of A091250. A132450(n) = a(n)-2^n, giving a more compact representation. Cf. A132447, similar, with no restriction on number of terms. Cf. A132451, similar, with restriction to exactly 5 terms. Cf. A132453, similar, with restriction to minimal number of terms.
%K nonn
%O 1,1
%A _Francois R. Grieu_, Aug 22 2007
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