A207192 Numbers that match odd polynomials among the monic polynomials over {-1,0,1}, ordered as at A206821.

2, 11, 13, 20, 57, 59, 65, 67, 90, 96, 98, 247, 249, 255, 257, 279, 281, 287, 289, 376, 382, 384, 406, 408, 414, 416, 1013, 1015, 1021, 1023, 1045, 1047, 1053, 1055, 1141, 1143, 1149, 1151, 1173, 1175, 1181, 1183, 1526, 1532, 1534, 1556, 1558

Offset

1,1

Comments

The polynomials y(k,x) range through all monic polynomials with coefficients in {-1,0,1}, ordered as at A206821.

Links

Table of n, a(n) for n=1..47.

Example

The first 13 polynomials:
1 .... 1
2 .... x
3 .... x + 1
4 .... x^2
5 .... x^2 - 1
6 .... x^2 - x
7 .... x^2 - x - 1
8 .... x^2 + 1
9 .... x^2 + x
10 ... x^2 + x + 1
11 ... x^3
12 ... x^3 - 1
13 ... x^3 - x
Numbers n for which y(n,-x)=y(n,x): 1,4,5,8,26,...
Numbers n for which y(n,-x)=-y(n,x): 2,11,13,20,...

Mathematica

t = Table[IntegerDigits[n, 2], {n, 1, 2000}];
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, 10}]
y = Flatten[y1]; (* polynomials over {-1, 0, 1} *)
Flatten[Position[y - (y /. x -> -x), 0]]  (* A207191 *)
Flatten[Position[y + (y /. x -> -x), 0]]  (* A207192  *)

Crossrefs

Cf. A206821.

Sequence in context: A167412 A166561 A179462 * A240097 A018375 A274408

Adjacent sequences: A207189 A207190 A207191 * A207193 A207194 A207195

Keyword

nonn

Author

Clark Kimberling, Feb 16 2012

Status

approved