OFFSET
1,1
COMMENTS
Church's table extends through degree 11.
REFERENCES
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 553-555.
LINKS
T. D. Noe, Table of n, a(n) for n=1..1377 (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, x+1; x^2+x+1; x^3+x+1, x^3+x^2+1; ... Note that x is irreducible but not primitive.
MATHEMATICA
Do[a = Reverse[ IntegerDigits[n, 2]]; b = {0}; l = Length[a]; k = 1; While[k < l + 1, b = Append[b, a[[k]]*x^(k - 1) ]; k++ ]; b = Apply[Plus, b]; c = Factor[b, Modulus -> 2]; If[b == c, Print[ FromDigits[ IntegerDigits[n, 2]]]], {n, 3, 250, 2} ]
PROG
(PARI)
seq(N, p=2, maxdeg=oo) = {
my(a = List(), k=0, d=0);
while (d++ <= maxdeg,
for (n=p^d, 2*p^d-1, my(f=Mod(Pol(digits(n, p)), p));
if(polisirreducible(f), listput(a, subst(lift(f), 'x, 10)); k++);
if(k >= N, break(2))));
Vec(a);
};
seq(27) \\ Gheorghe Coserea, May 28 2018
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jan 13 2001
STATUS
approved