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 A207189 Numbers matching polynomials y(k,x) that have x-1 as a factor; see Comments. 5
 5, 6, 12, 13, 15, 27, 28, 30, 34, 58, 59, 61, 65, 73, 121, 122, 124, 128, 136, 152, 248, 249, 251, 255, 263, 279, 311, 503, 504, 506, 510, 518, 534, 566, 630, 1014, 1015, 1017, 1021, 1029, 1045, 1077, 1141, 1269, 2037, 2038, 2040, 2044, 2052, 2068 (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..50. 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 The list exemplifies these sequences: A207187 (multiples of x + 1): 3,5,9,13,... A207188 (multiples of x): 2,4,6,9,11,13,... A207189 (multiples of x - 1): 5,6,12,13,... A207190 (multiples of x^2 + 1): 8,20,25,27,... 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} *) TableForm[Table[{n, y[[n]], Factor[y[[n]]]}, {n, 1, 10}]] Table[y[[n]] /. x -> -1, {n, 1, 300}]; Flatten[Position[%, 0]] (* A207187 *) Table[y[[n]] /. x -> 0, {n, 1, 300}] ; Flatten[Position[%, 0]] (* A207188 *) Table[y[[n]] /. x -> 1, {n, 1, 1200}] ; Flatten[Position[%, 0]] (* A207189 *) Table[y[[n]] /. x -> I, {n, 1, 600}] ; Flatten[Position[%, 0]] (* A207190 *) CROSSREFS Cf. A206821. Sequence in context: A177714 A273158 A099641 * A285404 A047319 A244368 Adjacent sequences: A207186 A207187 A207188 * A207190 A207191 A207192 KEYWORD nonn AUTHOR Clark Kimberling, Feb 16 2012 STATUS approved

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Last modified May 25 15:42 EDT 2024. Contains 372800 sequences. (Running on oeis4.)