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%I #22 Feb 16 2023 16:00:26
%S 1,2,5,10,3,4,6,8,12,15,20,24,30,40,60,120,7,14,19,35,38,70,95,133,
%T 190,266,665,1330,16,48,61,80,122,183,240,244,305,366,488,610,732,915,
%U 976,1220,1464,1830,2440,2928,3660,4880,7320,14640,25,50,3221,6442
%N Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(11) listed in ascending order.
%H Alois P. Heinz, <a href="/A218336/b218336.txt">Rows n = 1..23, flattened</a>
%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 T(n,k) = k-th smallest element of M(n) = {d : d|(11^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
%e Triangle begins:
%e 1, 2, 5, 10;
%e 3, 4, 6, 8, 12, 15, 20, 24, 30, 40, ...
%e 7, 14, 19, 35, 38, 70, 95, 133, 190, 266, ...
%e 16, 48, 61, 80, 122, 183, 240, 244, 305, 366, ...
%e 25, 50, 3221, 6442, 16105, 32210, 80525, 161050;
%e ...
%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 T:= n-> sort([M(n)[]])[]:
%p seq(T(n), n=1..5);
%t M[n_] := M[n] = Divisors[11^n - 1] ~Complement~ U[n-1];
%t U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t T[n_] := Sort[M[n]];
%t Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y Column k=5 of A212737.
%Y Last elements of rows give: A024127.
%Y Column k=1 gives: A218359.
%Y Row lengths are A212957(n,11).
%K nonn,look,tabf
%O 1,2
%A _Alois P. Heinz_, Oct 26 2012
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