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

1,1

Links

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

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 *)

Prog

(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)));

Crossrefs

Intersection of A091242 and A206074.

Subsequence: A260428.

Cf. also A260426, A206075.

Sequence in context: A022141 A322985 A240031 * A091209 A307471 A226671

Adjacent sequences: A260424 A260425 A260426 * A260428 A260429 A260430

Keyword

nonn

Author

Antti Karttunen, Jul 26 2015

Status

approved