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

%I #7 Sep 17 2013 05:24:23

%S 5,10,15,20,30,40,45,60,65,75,80,85,90,95,105,120,125,130,135,150,160,

%T 165,170,175,180,190,195,210,215,225,235,240,245,250,255,260,270,300,

%U 320,325,330,335,340,350,360,365,380,390,420,430,450,455,470

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

%C Is this a duplicate of A131853?

%C 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.

%t t = Table[IntegerDigits[n, 2], {n, 1, 3000}];

%t b[n_] := Reverse[Table[x^k, {k, 0, n}]]

%t p[n_, x_] := p[n, x] = t[[n]].b[-1 + Length[t[[n]]]]

%t TableForm[Table[{n, p[n, x], Factor[p[n, x]]},

%t {n, 1, 16}]]

%t u = {}; Do[n++; If[(p[n, x] /. x -> I) == 0,

%t AppendTo[u, n]], {n, 800}]

%t u (* A206715 *)

%t u/5 (* A206716 *)

%Y Cf. A131853, A206074, A206716.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 11 2012