A260428 Composite numbers whose binary representations encode a polynomial (with coefficients 0 or 1) which is irreducible over Q, but reducible over GF(2).

69, 77, 81, 121, 169, 205, 209, 261, 265, 275, 289, 295, 305, 321, 323, 327, 329, 339, 377, 405, 407, 437, 453, 473, 475, 481, 493, 517, 533, 551, 553, 559, 565, 575, 581, 583, 595, 625, 649, 667, 671, 689, 703, 707, 737, 747, 749, 755, 763, 767, 779, 781, 785, 805, 815, 833, 835, 851, 855, 861, 869, 893, 905

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..11585

Maple

f:= proc(n) local L, p, x;
  if isprime(n) then return false fi;
  L:= convert(n, base, 2);
  p:= add(L[i]*x^(i-1), i=1..nops(L));
  irreduc(p) and not (Irreduc(p) mod 2);
end proc:
select(f, [$2..10000]); # Robert Israel, Jul 27 2015

Mathematica

okQ[n_] := CompositeQ[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)
isA260428(n) = (polisirreducible( Pol(binary(n)) ) && !polisirreducible(Pol(binary(n))*Mod(1, 2)) && !isprime(n));
n = 0; i = 0; while(n < 65537, n++; if(isA260428(n), i++; write("b260428.txt", i, " ", n)));

Crossrefs

Intersection of A002808 and A260427.

Intersection of A091212 and A206074.

Intersection of A091242 and A206075.

Complement of A257688 in A206074.

Sequence in context: A166067 A253437 A325386 * A168477 A264045 A295806

Adjacent sequences: A260425 A260426 A260427 * A260429 A260430 A260431

Keyword

nonn

Author

Antti Karttunen, Jul 26 2015

Status

approved