This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132451 #8 May 06 2022 13:13:51 %S A132451 0,0,0,0,47,91,143,285,539,1051,2071,4179,8219,16427,32791,65581, %T A132451 131087,262183,524327,1048659,2097191,4194361,8388651,16777243, %U A132451 33554447,67108935,134217767,268435539,536870935,1073741907,2147483663 %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 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 A132451 <a href="/index/Ge#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. %K A132451 nonn %O A132451 1,5 %A A132451 Francois R. Grieu (f(AT)grieu.com), Aug 22 2007