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A207192 Numbers that match odd polynomials among the monic polynomials over {-1,0,1}, ordered as at A206821. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)