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Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X].
8

%I #8 Jun 08 2018 13:52:33

%S 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 31,31,31,31,31,37,37,37,37,37,37,41,41,41,41,47,47,47,47,47,47,55,55,

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

%C a(n) is the smallest term of A014580 greater than n.

%H Antti Karttunen, <a href="/A305420/b305420.txt">Table of n, a(n) for n = 1..21845</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>

%F For n >= 1, a(n) = A091228(1+n).

%o (PARI)

%o A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));

%o A305420(n) = { my(k=1+n); while(!A091225(k),k++); (k); };

%Y Cf. A014580, A091225, A091228, A305419, A305421.

%Y Cf. also A151800, A305430.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 07 2018