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A305420 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X].

%I A305420 #8 Jun 08 2018 13:52:33
%S A305420 2,3,7,7,7,7,11,11,11,11,13,13,19,19,19,19,19,19,25,25,25,25,25,25,31,
%T A305420 31,31,31,31,31,37,37,37,37,37,37,41,41,41,41,47,47,47,47,47,47,55,55,
%U A305420 55,55,55,55,55,55,59,59,59,59,61,61,67,67,67,67,67,67,73,73,73,73,73,73,87,87,87,87,87,87,87,87,87,87,87,87,87,87,91
%N A305420 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X].
%C A305420 a(n) is the smallest term of A014580 greater than n.
%H A305420 Antti Karttunen, <a href="/A305420/b305420.txt">Table of n, a(n) for n = 1..21845</a>
%H A305420 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A305420 For n >= 1, a(n) = A091228(1+n).
%o A305420 (PARI)
%o A305420 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305420 A305420(n) = { my(k=1+n); while(!A091225(k),k++); (k); };
%Y A305420 Cf. A014580, A091225, A091228, A305419, A305421.
%Y A305420 Cf. also A151800, A305430.
%K A305420 nonn
%O A305420 1,1
%A A305420 _Antti Karttunen_, Jun 07 2018