A206716 -id:A206716 - cp's OEIS frontend

A206715 Numbers matched to polynomials divisible by x^2+1.

5, 10, 15, 20, 30, 40, 45, 60, 65, 75, 80, 85, 90, 95, 105, 120, 125, 130, 135, 150, 160, 165, 170, 175, 180, 190, 195, 210, 215, 225, 235, 240, 245, 250, 255, 260, 270, 300, 320, 325, 330, 335, 340, 350, 360, 365, 380, 390, 420, 430, 450, 455, 470

Offset: 1

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Clark Kimberling, Feb 11 2012

nonn

Is this a duplicate of A131853?

The polynomials having coefficients in {0,1} are enumerated as in A206074. The sequence A206715 shows the numbers of those satisfying p(n,i)=0.

Cf. A131853, A206074, A206716.

t = Table[IntegerDigits[n, 2], {n, 1, 3000}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := p[n, x] = t[[n]].b[-1 + Length[t[[n]]]]
TableForm[Table[{n, p[n, x], Factor[p[n, x]]},
  {n, 1, 16}]]
u = {}; Do[n++; If[(p[n, x] /. x -> I) == 0,
  AppendTo[u, n]], {n, 800}]
u    (* A206715 *)
u/5  (* A206716 *)

cp's OEIS Frontend

A206715 Numbers matched to polynomials divisible by x^2+1.

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