OFFSET
1,1
COMMENTS
Church's table extends through degree 11.
LINKS
T. D. Noe, Table of n, a(n) for n=1..1110 (through degree 13)
R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
EXAMPLE
The first few are x+1; x^2+x+1; x^3+x+1, x^3+x^2+1; ... Note that x is irreducible but not primitive.
MATHEMATICA
car = 2; maxDegree = 13;
okQ[{1, 1}] = True;
okQ[coefs_List] := Module[{P}, P = coefs.x^Range[Length[coefs]-1, 0, -1]; coefs[[1]] == 1 && IrreduciblePolynomialQ[P, Modulus -> car] && PrimitivePolynomialQ[P, car]];
FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* Jean-François Alcover, Sep 09 2019 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jan 13 2001
STATUS
approved