Search: id:A132451
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%I A132451
%S A132451 0,0,0,0,47,91,143,285,539,1051,2071,4179,8219,16427,32791,65581,131087,
%T A132451 262183,524327,1048659,2097191,4194361,8388651,16777243,33554447,
%U A132451 67108935,134217767,268435539,536870935,1073741907,2147483663
%N A132451 First primitive GF(2)[X] polynomials of degree n with exactly 5 terms.
%C A132451 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 maxmimum-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 A132451 <a href="Sindx_Ge.html#GF2X">Index entries for sequences operating on 
               GF(2)[X]-polynomials</a>
%e A132451 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 A132451 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.
%Y A132451 Sequence in context: A033232 A146031 A139968 this_sequence A004943 A004963 
               A061153
%Y A132451 Adjacent sequences: A132448 A132449 A132450 this_sequence A132452 A132453 
               A132454
%K A132451 nonn
%O A132451 1,5
%A A132451 Francois R. Grieu (f(AT)grieu.com), Aug 22 2007

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