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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..53.

Mathematica

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 *)

Crossrefs

Cf. A131853, A206074, A206716.

Sequence in context: A356106 A178892 A269805 * A131853 A115817 A070004

Adjacent sequences: A206712 A206713 A206714 * A206716 A206717 A206718

Keyword

nonn

Author

Clark Kimberling, Feb 11 2012

Status

approved