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A206829 Number of distinct irreducible factors of the polynomial y(n,x) defined at A206821. 2
0, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 3, 3, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 4, 1, 3, 1, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The first 6 polynomials: 1, x, 1+x, x^2, x^2-1, x^2-x, representing an ordering of the monic polynomials having coefficients in {-1,0,1}; see A206821.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

y(5,x) = (x-1)(x+1), so a(5)=2.

MATHEMATICA

t = Table[IntegerDigits[n, 2], {n, 1, 1000}];

b[n_] := Reverse[Table[x^k, {k, 0, n}]]

p[n_] := p[n] = t[[n]].b[-1 + Length[t[[n]]]]

TableForm[Table[{n, p[n], Factor[p[n]]}, {n, 1, 6}]]

f[k_] := 2^k - k; g[k_] := 2^k - 2 + f[k - 1];

q1[n_] := p[2^(k - 1)] - p[n + 1 - f[k]]

q2[n_] := p[n - f[k] + 2]

y1 = Table[p[n], {n, 1, 4}];

Do[AppendTo[y1, Join[Table[q1[n], {n, f[k], g[k] - 1}],

   Table[q2[n], {n, g[k], f[k + 1] - 1}]]], {k, 3, 8}]

y = Flatten[y1]; (* polynomials over {-1, 0, 1} *)

TableForm[Table[{n, y[[n]], Factor[y[[n]]]}, {n, 1, 10}]]

Table[-1 + Length[FactorList[y[[n]]]],

{n, 1, 120}]  (* A206829 *)

CROSSREFS

Cf. A206821.

Sequence in context: A202205 A336123 A075661 * A319694 A335641 A163495

Adjacent sequences:  A206826 A206827 A206828 * A206830 A206831 A206832

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 12 2012

STATUS

approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)