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A305430 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.

%I A305430 #10 Dec 20 2021 09:47:09
%S A305430 2,3,5,5,7,7,11,11,11,11,13,13,17,17,17,17,19,19,23,23,23,23,25,25,29,
%T A305430 29,29,29,31,31,37,37,37,37,37,37,41,41,41,41,43,43,47,47,47,47,53,53,
%U A305430 53,53,53,53,55,55,59,59,59,59,61,61,67,67,67,67,67,67,69,69,71,71,73,73,77,77,77,77,79,79,81,81,83,83,87,87,87,87,89,89
%N A305430 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.
%C A305430 a(n) is the smallest term of A206074 greater than n.
%H A305430 Antti Karttunen, <a href="/A305430/b305430.txt">Table of n, a(n) for n = 1..21845</a>
%t A305430 binPol[n_, x_] := With[{bb = IntegerDigits[n, 2]},bb.x^Range[Length[bb]-1, 0, -1]];
%t A305430 b[n_] := If[IrreduciblePolynomialQ[binPol[n, x]], 1, 0];
%t A305430 a[n_] := Module[{k = n+1}, While[b[k] == 0, k++]; k];
%t A305430 Array[a, 100] (* _Jean-François Alcover_, Dec 20 2021 *)
%o A305430 (PARI)
%o A305430 A257000(n) = polisirreducible(Pol(binary(n)));
%o A305430 A305430(n) = { my(k=1+n); while(!A257000(k),k++); (k); };
%Y A305430 Cf. A206074, A257000, A305429.
%Y A305430 Cf. also A151800, A305420.
%K A305430 nonn
%O A305430 1,1
%A A305430 _Antti Karttunen_, Jun 07 2018