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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..79.

FORMULA

Integers in A000027 but not in A267509

EXAMPLE

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.

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.

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-Fran├žois Alcover, Feb 01 2016 *)

CROSSREFS

Sequence in context: A182483 A323013 A163975 * A202267 A125975 A046758

Adjacent sequences:  A267518 A267519 A267520 * A267522 A267523 A267524

KEYWORD

nonn,base

AUTHOR

Abdul Gaffar Khan, Jan 16 2016

STATUS

approved

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Last modified March 21 20:15 EDT 2019. Contains 321382 sequences. (Running on oeis4.)