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%I #15 Feb 06 2023 05:02:09
%S 5,17,23,29,43,53,69,71,77,79,81,83,89,101,107,113,121,127,139,149,
%T 151,163,169,173,179,181,197,199,205,209,223,227,233,251,257,261,263,
%U 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
%N Binary codes for polynomials (with coefficients 0 or 1) that are irreducible over Q, but reducible over GF(2).
%H Antti Karttunen, <a href="/A260427/b260427.txt">Table of n, a(n) for n = 1..16972</a>
%t 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]];
%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Feb 06 2023 *)
%o (PARI)
%o isA260427(n) = (polisirreducible( Pol(binary(n)) ) && !polisirreducible(Pol(binary(n))*Mod(1, 2)));
%o n = 0; i = 0; while(n < 65537, n++; if(isA260427(n), i++; write("b260427.txt", i, " ", n)));
%Y Intersection of A091242 and A206074.
%Y Subsequence: A260428.
%Y Cf. also A260426, A206075.
%K nonn
%O 1,1
%A _Antti Karttunen_, Jul 26 2015
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