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Coefficients of monic irreducible polynomials over GF(5) listed in lexicographic order.
13

%I #16 Sep 29 2020 17:01:52

%S 10,11,12,13,14,102,103,111,112,123,124,133,134,141,142,1011,1014,

%T 1021,1024,1032,1033,1042,1043,1101,1102,1113,1114,1131,1134,1141,

%U 1143,1201,1203,1213,1214,1222,1223,1242,1244,1302,1304,1311,1312,1322,1323,1341

%N Coefficients of monic irreducible polynomials over GF(5) listed in lexicographic order.

%C Church's table extends through degree 5.

%D R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 557-560.

%H T. D. Noe, <a href="/A058945/b058945.txt">Table of n, a(n) for n=1..63319</a> (through degree 8)

%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 A058945 = Union[ Reap[ Do[ a = Reverse[ IntegerDigits[n, 5]]; 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 -> 5]; id = IntegerDigits[n, 5]; If[b == c && (id == {1, 0} || id[[-1]] != 0), Sow[ FromDigits[id] ] ], {n, 5, 300}]][[2, 1]]](* _Jean-François Alcover_, Feb 13 2012, after A058943 *)

%Y Cf. A058943, A058944, A058946, A058947, A058948.

%Y Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, this sequence, A058946. 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