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A058950
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Coefficients of monic primitive irreducible polynomials over GF(5) listed in lexicographic order.
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11
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12, 13, 112, 123, 133, 142, 1032, 1033, 1042, 1043, 1102, 1113, 1143, 1203, 1213, 1222, 1223, 1242, 1302, 1312, 1322, 1323, 1343, 1403, 1412, 1442, 10122, 10123, 10132, 10133, 10412, 10413, 10442, 10443, 11013, 11023, 11032, 11042, 11113
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OFFSET
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1,1
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..354 (through degree 5)
R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. Church's table extends through degree 5.
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MATHEMATICA
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car = 5; maxDegree = 5;
okQ[coefs_List] := Module[{P}, P = coefs.x^Range[Length[coefs] - 1, 0, -1]; coefs[[1]] == 1 && IrreduciblePolynomialQ[P, Modulus -> car] && PrimitivePolynomialQ[P, car]];
FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* Jean-François Alcover, Sep 10 2019 *)
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CROSSREFS
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Cf. A058945.
Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, A058945, A058946. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.
Sequence in context: A085546 A041306 A058952 * A064003 A135123 A129476
Adjacent sequences: A058947 A058948 A058949 * A058951 A058952 A058953
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane, Jan 13 2001
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EXTENSIONS
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More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006
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STATUS
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approved
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