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A305419 Largest k < n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X], with a(1) = a(2) = 1.

%I A305419 #8 Jun 08 2018 13:52:27
%S A305419 1,1,2,3,3,3,3,7,7,7,7,11,11,13,13,13,13,13,13,19,19,19,19,19,19,25,
%T A305419 25,25,25,25,25,31,31,31,31,31,31,37,37,37,37,41,41,41,41,41,41,47,47,
%U A305419 47,47,47,47,47,47,55,55,55,55,59,59,61,61,61,61,61,61,67,67,67,67,67,67,73,73,73,73,73,73,73,73,73,73,73,73,73,73,87
%N A305419 Largest k < n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X], with a(1) = a(2) = 1.
%C A305419 For n >= 3, a(n) is the largest term of A014580 less than n.
%H A305419 Antti Karttunen, <a href="/A305419/b305419.txt">Table of n, a(n) for n = 1..21845</a>
%H A305419 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%o A305419 (PARI)
%o A305419 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305419 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%Y A305419 Cf. A014580, A091225, A305420, A305422.
%Y A305419 Cf. also A151799 (A136548), A305429.
%K A305419 nonn
%O A305419 1,3
%A A305419 _Antti Karttunen_, Jun 07 2018