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%I #19 Jun 29 2019 02:20:43
%S 1,2,3,5,7,10,11,12,13,14,15,16,17,18,19,21,23,25,27,29,31,32,34,35,
%T 37,38,41,43,45,47,49,51,52,53,53,56,57,58,59,61,65,67,71,72,73,74,75,
%U 76,78,79,81,83,85,87,89,91,92,94,95,97,98,101,102,103,104,105,106,107,108,109,111,112,113,114,115,116,117,118,119
%N Integers whose base-10 representation (Bm,...,B1,B0) is such that the polynomial f(x) = B0 + B1*x + ... + Bm*x^m is irreducible over the ring of integers, 0 <= Bi <= 9.
%F Integers in A000027 but not in A267509.
%e 11 is a member as f(x) = B0 + B1*x = 1 + 1*x has no factorization other than the trivial one, i.e., 1*(1+x), hence f(x) is irreducible over the ring of integers.
%e 114 is a member as f(x) = B0 + B1*x + B2*x^2 = 4 + 1*x + 1*x^2 = 4 + x + x^2 is irreducible over the ring of integers.
%t okQ[n_] := If[n<10, !CompositeQ[n], !MatchQ[Factor[(id = IntegerDigits[n]). x^Range[Length[id]-1, 0, -1]][[0]], Times|Power]]; Select[Range[120], okQ] (* _Jean-François Alcover_, Feb 01 2016 *)
%K nonn,base
%O 1,2
%A _Abdul Gaffar Khan_, Jan 16 2016
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