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A218356 Minimal order of degree-n irreducible polynomials over GF(3). 7
1, 4, 13, 5, 11, 7, 1093, 32, 757, 44, 23, 35, 797161, 547, 143, 17, 1871, 19, 1597, 25, 14209, 67, 47, 224, 8951, 398581, 109, 29, 59, 31, 683, 128, 299, 103, 71, 95, 13097927, 2851, 169, 352, 83, 43, 431, 115, 181, 188, 1223, 97, 491, 151, 12853, 53, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) < 3^n.
For n > 2, a(n) <= A143663(n). For odd prime n, a(n) = A143663(n). - Max Alekseyev, Apr 30 2022
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..796 (first 100 terms from Alois P. Heinz)
FORMULA
a(n) = min(M(n)) with M(n) = {d : d|(3^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
a(n) = A212906(n,1) = A213224(n,2).
MAPLE
M:= proc(n) M(n):= numtheory[divisors](3^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..60);
MATHEMATICA
M[n_] := M[n] = Divisors[3^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, 60}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A170865 A320030 A191509 * A249120 A170844 A051432
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 27 2012
STATUS
approved

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Last modified February 26 02:19 EST 2024. Contains 370335 sequences. (Running on oeis4.)