A058946 - OEIS

A058946

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

10, 11, 12, 13, 14, 15, 16, 101, 102, 104, 113, 114, 116, 122, 123, 125, 131, 135, 136, 141, 145, 146, 152, 153, 155, 163, 164, 166, 1002, 1003, 1004, 1005, 1011, 1016, 1021, 1026, 1032, 1035, 1041, 1046, 1052, 1055, 1062, 1065, 1101, 1103, 1112, 1115

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OFFSET

1,1

COMMENTS

Church's table extends through degree 3.

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n=1..728 (through degree 4)

R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.

MATHEMATICA

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 *)

CROSSREFS

Cf. A058943, A058944, A058945, A058947.

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.

Sequence in context: A124367 A008711 A008710 * A118379 A174397 A297266

Adjacent sequences: A058943 A058944 A058945 * A058947 A058948 A058949

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Jan 13 2001

EXTENSIONS

More terms from David Wasserman, May 23 2002

STATUS

approved