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

1,2

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A206074.

Sequence in context: A157269 A371129 A186892 * A276448 A176275 A108166

Adjacent sequences: A206072 A206073 A206074 * A206076 A206077 A206078

Keyword

nonn

Author

Clark Kimberling, Feb 03 2012

Status

approved