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A218359 Minimal order of degree-n irreducible polynomials over GF(11). 2


%S 1,3,7,16,25,9,43,32,1772893,75,15797,13,1093,129,175,17,

%T 50544702849929377,27,6115909044841454629,400,49,23,829,224,125,53,

%U 5559917315850179173,29,523,31,50159,128,661,71707,211,351,2591,191,79,41,83,147,1416258521793067

%N Minimal order of degree-n irreducible polynomials over GF(11).

%C a(n) < 11^n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>

%F 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) = {}.

%F a(n) = A218336(n,1) = A213224(n,5).

%p with(numtheory):

%p M:= proc(n) M(n):= divisors(11^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..42);

%Y Cf. A213224, A218336.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 27 2012

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Last modified February 24 04:35 EST 2020. Contains 332197 sequences. (Running on oeis4.)