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A218362 Minimal order of degree-n irreducible polynomials over GF(19). 4
1, 4, 27, 16, 151, 7, 701, 17, 81, 11, 104281, 13, 599, 197, 31, 64, 3044803, 199, 109912203092239643840221, 176, 18927, 23, 277, 119, 101, 131, 243, 29, 59, 61, 243270318891483838103593381595151809701, 97, 67, 12179212, 71, 37, 149, 108301, 79, 41, 10654507 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) < 19^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|(19^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
a(n) = A218339(n,1) = A213224(n,8).
MAPLE
with(numtheory):
M:= proc(n) M(n):= divisors(19^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..28);
MATHEMATICA
M[n_] := M[n] = Divisors[19^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, 41}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A125723 A094543 A136511 * A108138 A119361 A133482
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 27 2012
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)