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A267521 Integers n having base 10 representation (Bm,...,B1,B0) such that the polynomial f(x)=B0+B1x+...+Bmx^m is irreducible over the ring of integers, 0<=Bi<=9 0

%I

%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 n having base 10 representation (Bm,...,B1,B0) such that the polynomial f(x)=B0+B1x+...+Bmx^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+B1x=1+1x 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+B1x+B2x^2=4+1x+1x^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-Fran├žois Alcover_, Feb 01 2016 *)

%K nonn,base

%O 1,2

%A _Abdul Gaffar Khan_, Jan 16 2016

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)