A058945 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

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 *)

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.

Sequence in context: A073527 A008707 A089951 * A270040 A339093 A072554

Adjacent sequences: A058942 A058943 A058944 * A058946 A058947 A058948

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Jan 13 2001

EXTENSIONS

More terms from David Wasserman, May 23 2002

STATUS

approved