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Search: id:A058943
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| A058943 |
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Coefficients of irreducible polynomials over GF(2) listed in lexicographic order. |
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+0
19
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| 10, 11, 111, 1011, 1101, 10011, 11001, 11111, 100101, 101001, 101111, 110111, 111011, 111101, 1000011, 1001001, 1010111, 1011011, 1100001, 1100111, 1101101, 1110011, 1110101, 10000011, 10001001, 10001111, 10010001
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 553-555.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1377 (through degree 13)
F. Ruskey, Irreducible and Primitive Polynomials over GF(2)
Index entries for sequences containing GF(2)[X]-polynomials
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EXAMPLE
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The first few are x, x+1; x^2+x+1; x^3+x+1, x^3+x^2+1; ... Note that x is irreducible but not primitive.
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MATHEMATICA
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Do[a = Reverse[ IntegerDigits[n, 2]]; b = {0}; l = Length[a]; k = 1; While[k < l + 1, b = Append[b, a[[k]]*x^(k - 1) ]; k++ ]; b = Apply[Plus, b]; c = Factor[b, Modulus -> 2]; If[b == c, Print[ FromDigits[ IntegerDigits[n, 2]]]], {n, 3, 250, 2} ]
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CROSSREFS
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Cf. A000020, A001037, A011260, A058944-A058948.
Converted to decimal: A014580.
Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): this sequence, 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: A035526 A164370 A059458 this_sequence A041217 A041218 A041917
Adjacent sequences: A058940 A058941 A058942 this_sequence A058944 A058945 A058946
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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 (njas(AT)research.att.com), Jan 13 2001
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EXTENSIONS
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Church's table extends through degree 11.
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