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A218359
Minimal order of degree-n irreducible polynomials over GF(11).
4
1, 3, 7, 16, 25, 9, 43, 32, 1772893, 75, 15797, 13, 1093, 129, 175, 17, 50544702849929377, 27, 6115909044841454629, 400, 49, 23, 829, 224, 125, 53, 5559917315850179173, 29, 523, 31, 50159, 128, 661, 71707, 211, 351, 2591, 191, 79, 41, 83, 147, 1416258521793067
OFFSET
1,2
COMMENTS
a(n) < 11^n.
LINKS
Eric Weisstein's World of Mathematics, Irreducible Polynomial
Eric Weisstein's World of Mathematics, Polynomial Order
FORMULA
a(n) = min(M(n)) with M(n) = {d : d|(11^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
a(n) = A218336(n,1) = A213224(n,5).
MAPLE
with(numtheory):
M:= proc(n) M(n):= divisors(11^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..42);
MATHEMATICA
M[n_] := M[n] = Divisors[11^n - 1]~Complement~U[n - 1];
U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
a[n_] := Min[M[n]];
Table[a[n], {n, 1, 43}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 27 2012
STATUS
approved