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A218356 Minimal order of degree-n irreducible polynomials over GF(3). 3


%S 1,4,13,5,11,7,1093,32,757,44,23,35,797161,547,143,17,1871,19,1597,25,

%T 14209,67,47,224,8951,398581,109,29,59,31,683,128,299,103,71,95,

%U 13097927,2851,169,352,83,43,431,115,181,188,1223,97,491,151,12853,53,107

%N Minimal order of degree-n irreducible polynomials over GF(3).

%C a(n) < 3^n.

%H Alois P. Heinz, <a href="/A218356/b218356.txt">Table of n, a(n) for n = 1..100</a>

%F 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) = {}.

%F a(n) = A212906(n,1) = A213224(n,2).

%p M:= proc(n) M(n):= divisors(3^n-1) minus U(n-1) end:

%p U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:

%p a:= n-> min(M(n)[]):

%p seq (a(n), n=1..60);

%Y Cf. A212906, A213224.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 27 2012

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Last modified January 25 07:47 EST 2020. Contains 331241 sequences. (Running on oeis4.)