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A207669 Numbers that match polynomomials 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

Table of n, a(n) for n=1..59.

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 A047563

Adjacent sequences:  A207666 A207667 A207668 * A207670 A207671 A207672

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 26 2012

STATUS

approved

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Last modified August 23 01:10 EDT 2019. Contains 326211 sequences. (Running on oeis4.)