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A206075 Nonprimes in A206074 (a coding of irreducible polynomials).

%I A206075 #7 May 14 2015 15:48:56
%S A206075 1,25,55,69,77,81,87,91,115,117,121,143,145,169,171,185,203,205,209,
%T A206075 213,247,253,261,265,275,285,289,295,299,301,305,319,321,323,327,329,
%U A206075 333,339,351,355,357,361,369,375,377,391,395,405,407,415,425,437
%N A206075 Nonprimes in A206074 (a coding of irreducible polynomials).
%H A206075 Charles R Greathouse IV, <a href="/A206075/b206075.txt">Table of n, a(n) for n = 1..10000</a>
%e A206075 Under the coding of irreducible polynomials over {0,1} which is given at A206074, the polynomials matching the first five terms of A206075 are indicated here:
%e A206075 1 .... 1
%e A206075 25 ... x^4 + x^3 + 1
%e A206075 55 ... x^5 + x^4 + x^2 + x + 1
%e A206075 69 ... x^6 + x^2 + 1
%e A206075 77 ... x^6 + x^3 + x^2 + 1
%t A206075 t = Table[IntegerDigits[n, 2], {n, 1, 1500}];
%t A206075 b[n_] := Reverse[Table[x^k, {k, 0, n}]]
%t A206075 p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
%t A206075 u = {1}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]], AppendTo[u, n]], {n, 1000}]
%t A206075 nonprimes = Complement[Range[800], Table[Prime[n], {n, 1, 800}]];
%t A206075 Intersection[u, nonprimes]  (* A206075 *)
%o A206075 (PARI) is(n)=n==1 || (polisirreducible( Pol(binary(n)) ) && !isprime(n)) \\ _Charles R Greathouse IV_, May 14 2015
%Y A206075 Cf. A206074.
%K A206075 nonn
%O A206075 1,2
%A A206075 _Clark Kimberling_, Feb 03 2012