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A207669 Numbers that match polynomials irreducible (mod 3), with coefficients in {0,1,2}. 5
3, 4, 5, 6, 7, 8, 10, 14, 17, 20, 22, 25, 34, 35, 38, 41, 43, 46, 49, 53, 58, 59, 65, 67, 71, 73, 77, 79, 86, 89, 92, 94, 97, 101, 110, 115, 118, 121, 125, 134, 137, 139, 145, 149, 151, 158, 166, 169, 172, 181, 185, 188, 190, 197, 205, 209, 212, 214, 217 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For such polynomials irreducible over the field of rational numbers, see A207966, which also describes the enumeration of all the nonzero polynomials whose coefficients are all in {0,1,2}.
LINKS
EXAMPLE
Polynomials having coefficients in {0,1,2} are
enumerated by the positive integers as follows:
n ... p[n,x] .. irreducible (mod 3)
1 ... 1 ....... no
2 ... 2 ....... no
3 ... x ....... yes
4 ... x+1 ..... yes
5 ... x+2 ..... yes
6 ... 2x ...... yes
7 ... 2x+1 .... yes
8 ... 2x+2 .... yes
9 ... x^2 ..... no
10 .. x^2+1 ... yes
11 .. x^2+2 ... no
The least n for which p(n,x) is irreducible over the
rationals but not modulo 3 is 13; the factorization of
p(13,x) is (x+1)(x+2) (mod 3).
MATHEMATICA
t = Table[IntegerDigits[n, 3], {n, 1, 1000}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 15}]
u = {}; Do[n++;
If[IrreduciblePolynomialQ[p[n, x], Modulus -> 3],
AppendTo[u, n]], {n, 1, 400}]
u (* A207669 *)
Complement[Range[200], %] (* A207670 *)
b[n_] := FromDigits[IntegerDigits[u, 3][[n]]]
Table[b[n], {n, 1, 50}] (* A207671 *)
CROSSREFS
Cf. A207670 (complement), A207671 (ternary).
Sequence in context: A073632 A066378 A125684 * A001272 A273664 A364099
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 26 2012
STATUS
approved

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Last modified July 21 14:09 EDT 2024. Contains 374474 sequences. (Running on oeis4.)