A260427 Binary codes for polynomials (with coefficients 0 or 1) that are irreducible over Q, but reducible over GF(2).

5, 17, 23, 29, 43, 53, 69, 71, 77, 79, 81, 83, 89, 101, 107, 113, 121, 127, 139, 149, 151, 163, 169, 173, 179, 181, 197, 199, 205, 209, 223, 227, 233, 251, 257, 261, 263, 265, 269, 271, 275, 277, 281, 289, 293, 295, 305, 307, 311, 317, 321, 323, 327, 329, 331, 337, 339, 347, 349, 353, 359, 367, 373, 377, 383, 389, 401

Offset: 1

Author

Antti Karttunen, Jul 26 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16972

Crossrefs

Intersection of A091242 and A206074.

Subsequence: A260428.

Cf. also A260426, A206075.

Programs

Mathematica

okQ[n_] := Module[{id, pol, x}, id = IntegerDigits[n, 2] // Reverse; pol = id.x^Range[0, Length[id] - 1]; IrreduciblePolynomialQ[pol] && !IrreduciblePolynomialQ[pol, Modulus -> 2]];
Select[Range[1000], okQ] (* Jean-François Alcover, Feb 06 2023 *)

PARI

isA260427(n) = (polisirreducible( Pol(binary(n)) ) && !polisirreducible(Pol(binary(n))*Mod(1, 2)));
n = 0; i = 0; while(n < 65537, n++; if(isA260427(n), i++; write("b260427.txt", i, " ", n)));