A267521 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.

1, 2, 3, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 31, 32, 34, 35, 37, 38, 41, 43, 45, 47, 49, 51, 52, 53, 53, 56, 57, 58, 59, 61, 65, 67, 71, 72, 73, 74, 75, 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

Offset: 1

Author

Abdul Gaffar Khan, Jan 16 2016

Keywords

• nonn
• base

Examples

			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.
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.
		

Programs

Mathematica

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 *)

Formula

Integers in A000027 but not in A267509.