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

%I A207192 #5 Mar 30 2012 18:58:12
%S A207192 2,11,13,20,57,59,65,67,90,96,98,247,249,255,257,279,281,287,289,376,
%T A207192 382,384,406,408,414,416,1013,1015,1021,1023,1045,1047,1053,1055,1141,
%U A207192 1143,1149,1151,1173,1175,1181,1183,1526,1532,1534,1556,1558
%N A207192 Numbers that match odd polynomials among the monic polynomials over {-1,0,1}, ordered as at A206821.
%C A207192 The polynomials y(k,x) range through all monic polynomials with coefficients in {-1,0,1}, ordered as at A206821.
%e A207192 The first 13 polynomials:
%e A207192 1 .... 1
%e A207192 2 .... x
%e A207192 3 .... x + 1
%e A207192 4 .... x^2
%e A207192 5 .... x^2 - 1
%e A207192 6 .... x^2 - x
%e A207192 7 .... x^2 - x - 1
%e A207192 8 .... x^2 + 1
%e A207192 9 .... x^2 + x
%e A207192 10 ... x^2 + x + 1
%e A207192 11 ... x^3
%e A207192 12 ... x^3 - 1
%e A207192 13 ... x^3 - x
%e A207192 Numbers n for which y(n,-x)=y(n,x): 1,4,5,8,26,...
%e A207192 Numbers n for which y(n,-x)=-y(n,x): 2,11,13,20,...
%t A207192 t = Table[IntegerDigits[n, 2], {n, 1, 2000}];
%t A207192 b[n_] := Reverse[Table[x^k, {k, 0, n}]]
%t A207192 p[n_] := p[n] = t[[n]].b[-1 + Length[t[[n]]]]
%t A207192 TableForm[Table[{n, p[n], Factor[p[n]]}, {n, 1, 6}]]
%t A207192 f[k_] := 2^k - k; g[k_] := 2^k - 2 + f[k - 1];
%t A207192 q1[n_] := p[2^(k - 1)] - p[n + 1 - f[k]]
%t A207192 q2[n_] := p[n - f[k] + 2]
%t A207192 y1 = Table[p[n], {n, 1, 4}];
%t A207192 Do[AppendTo[y1,
%t A207192   Join[Table[q1[n], {n, f[k], g[k] - 1}],
%t A207192    Table[q2[n], {n, g[k], f[k + 1] - 1}]]], {k, 3, 10}]
%t A207192 y = Flatten[y1]; (* polynomials over {-1,0,1} *)
%t A207192 Flatten[Position[y - (y /. x -> -x), 0]]  (* A207191 *)
%t A207192 Flatten[Position[y + (y /. x -> -x), 0]]  (* A207192  *)
%Y A207192 Cf. A206821.
%K A207192 nonn
%O A207192 1,1
%A A207192 _Clark Kimberling_, Feb 16 2012