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A058943 Coefficients of irreducible polynomials over GF(2) listed in lexicographic order.

%I A058943 #15 May 28 2018 19:44:45
%S A058943 10,11,111,1011,1101,10011,11001,11111,100101,101001,101111,110111,
%T A058943 111011,111101,1000011,1001001,1010111,1011011,1100001,1100111,
%U A058943 1101101,1110011,1110101,10000011,10001001,10001111,10010001
%N A058943 Coefficients of irreducible polynomials over GF(2) listed in lexicographic order.
%C A058943 Church's table extends through degree 11.
%D A058943 R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 553-555.
%H A058943 T. D. Noe, <a href="/A058943/b058943.txt">Table of n, a(n) for n=1..1377</a> (through degree 13)
%H A058943 R. Church, <a href="http://www.jstor.org/stable/1968675">Tables of irreducible polynomials for the first four prime moduli</a>, Annals Math., 36 (1935), 198-209.
%H A058943 F. Ruskey, <a href="http://www.theory.cs.uvic.ca/~cos/gen/poly.html">Irreducible and Primitive Polynomials over GF(2)</a>
%H A058943 <a href="/index/Ge#GF2X">Index entries for sequences containing GF(2)[X]-polynomials</a>
%e A058943 The first few are x, x+1; x^2+x+1; x^3+x+1, x^3+x^2+1; ... Note that x is irreducible but not primitive.
%t A058943 Do[a = Reverse[ IntegerDigits[n, 2]]; b = {0}; l = Length[a]; k = 1; While[k < l + 1, b = Append[b, a[[k]]*x^(k - 1) ]; k++ ]; b = Apply[Plus, b]; c = Factor[b, Modulus -> 2]; If[b == c, Print[ FromDigits[ IntegerDigits[n, 2]]]], {n, 3, 250, 2} ]
%o A058943 (PARI)
%o A058943 seq(N, p=2, maxdeg=oo) = {
%o A058943   my(a = List(), k=0, d=0);
%o A058943   while (d++ <= maxdeg,
%o A058943     for (n=p^d, 2*p^d-1, my(f=Mod(Pol(digits(n,p)),p));
%o A058943       if(polisirreducible(f), listput(a, subst(lift(f),'x,10)); k++);
%o A058943       if(k >= N, break(2))));
%o A058943   Vec(a);
%o A058943 };
%o A058943 seq(27) \\ _Gheorghe Coserea_, May 28 2018
%Y A058943 Cf. A000020, A001037, A011260, A058944-A058948.
%Y A058943 Converted to decimal: A014580.
%Y A058943 Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): this sequence, A058944, A058948, A058945, A058946. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.
%K A058943 nonn,easy,nice
%O A058943 1,1
%A A058943 _N. J. A. Sloane_, Jan 13 2001