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

1, 25, 55, 69, 77, 81, 87, 91, 115, 117, 121, 143, 145, 169, 171, 185, 203, 205, 209, 213, 247, 253, 261, 265, 275, 285, 289, 295, 299, 301, 305, 319, 321, 323, 327, 329, 333, 339, 351, 355, 357, 361, 369, 375, 377, 391, 395, 405, 407, 415, 425, 437

Offset: 1

Author

Clark Kimberling, Feb 03 2012

Keywords

• nonn

Examples

			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:
1 .... 1
25 ... x^4 + x^3 + 1
55 ... x^5 + x^4 + x^2 + x + 1
69 ... x^6 + x^2 + 1
77 ... x^6 + x^3 + x^2 + 1
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A206074.

Programs

Mathematica

t = Table[IntegerDigits[n, 2], {n, 1, 1500}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
u = {1}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]], AppendTo[u, n]], {n, 1000}]
nonprimes = Complement[Range[800], Table[Prime[n], {n, 1, 800}]];
Intersection[u, nonprimes]  (* A206075 *)

PARI

is(n)=n==1 || (polisirreducible( Pol(binary(n)) ) && !isprime(n)) \\ Charles R Greathouse IV, May 14 2015