

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
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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



