A058945 Coefficients of monic irreducible polynomials over GF(5) listed in lexicographic order.

10, 11, 12, 13, 14, 102, 103, 111, 112, 123, 124, 133, 134, 141, 142, 1011, 1014, 1021, 1024, 1032, 1033, 1042, 1043, 1101, 1102, 1113, 1114, 1131, 1134, 1141, 1143, 1201, 1203, 1213, 1214, 1222, 1223, 1242, 1244, 1302, 1304, 1311, 1312, 1322, 1323, 1341

Offset: 1

Author

N. J. A. Sloane, Jan 13 2001

Keywords

• nonn
• easy
• nice

Comments

Church's table extends through degree 5.

References

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

Links

• T. D. Noe, Table of n, a(n) for n=1..63319 (through degree 8)
• R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.

Crossrefs

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

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.

Programs

Mathematica

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 *)

Extensions

More terms from David Wasserman, May 23 2002