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Coefficients of monic irreducible polynomials over GF(7) listed in lexicographic order.
15

%I #15 Sep 29 2020 17:03:07

%S 10,11,12,13,14,15,16,101,102,104,113,114,116,122,123,125,131,135,136,

%T 141,145,146,152,153,155,163,164,166,1002,1003,1004,1005,1011,1016,

%U 1021,1026,1032,1035,1041,1046,1052,1055,1062,1065,1101,1103,1112,1115

%N Coefficients of monic irreducible polynomials over GF(7) listed in lexicographic order.

%C Church's table extends through degree 3.

%D R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 560-562.

%H T. D. Noe, <a href="/A058946/b058946.txt">Table of n, a(n) for n=1..728</a> (through degree 4)

%H 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.

%t A058946 = Union[ Reap[ Do[ a = Reverse[ IntegerDigits[n, 7]]; b = {0}; la = Length[a]; k = 1; While[k < la + 1, b = Append[b, a[[k]]*x^(k - 1)]; k++]; b = Plus @@ b; c = Factor[b, Modulus -> 7]; id = IntegerDigits[n, 7]; If[b == c && (id == {1, 0} || id[[-1]] != 0), Sow[ FromDigits[id]]], {n, 7, 450}]][[2, 1]]](* _Jean-François Alcover_, Feb 13 2012, after A058943 *)

%Y Cf. A058943, A058944, A058945, A058947.

%Y Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, A058945, this sequence. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_, Jan 13 2001

%E More terms from _David Wasserman_, May 23 2002