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 A058943 Coefficients of irreducible polynomials over GF(2) listed in lexicographic order. 22
 10, 11, 111, 1011, 1101, 10011, 11001, 11111, 100101, 101001, 101111, 110111, 111011, 111101, 1000011, 1001001, 1010111, 1011011, 1100001, 1100111, 1101101, 1110011, 1110101, 10000011, 10001001, 10001111, 10010001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Church's table extends through degree 11. REFERENCES R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 553-555. LINKS T. D. Noe, Table of n, a(n) for n=1..1377 (through degree 13) R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. EXAMPLE 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. MATHEMATICA 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} ] PROG (PARI) seq(N, p=2, maxdeg=oo) = {   my(a = List(), k=0, d=0);   while (d++ <= maxdeg,     for (n=p^d, 2*p^d-1, my(f=Mod(Pol(digits(n, p)), p));       if(polisirreducible(f), listput(a, subst(lift(f), 'x, 10)); k++);       if(k >= N, break(2))));   Vec(a); }; seq(27) \\ Gheorghe Coserea, May 28 2018 CROSSREFS Cf. A000020, A001037, A011260, A058944-A058948. Converted to decimal: A014580. 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. Sequence in context: A287948 A287626 A059458 * A222473 A041217 A041218 Adjacent sequences:  A058940 A058941 A058942 * A058944 A058945 A058946 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Jan 13 2001 STATUS approved

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Last modified January 21 13:25 EST 2019. Contains 319350 sequences. (Running on oeis4.)