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A218340 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(23) listed in ascending order.

%I A218340 #25 Feb 16 2025 08:33:18
%S A218340 1,2,11,22,3,4,6,8,12,16,24,33,44,48,66,88,132,176,264,528,7,14,77,79,
%T A218340 154,158,553,869,1106,1738,6083,12166,5,10,15,20,30,32,40,53,55,60,80,
%U A218340 96,106,110,120,159,160,165,212,220,240,265,318,330,352,424,440
%N A218340 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(23) listed in ascending order.
%H A218340 Alois P. Heinz, <a href="/A218340/b218340.txt">Rows n = 1..17, flattened</a>
%H A218340 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218340 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218340 T(n,k) = k-th smallest element of M(n) = {d : d|(23^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
%e A218340 Triangle begins:
%e A218340        1,      2,      11,      22;
%e A218340        3,      4,       6,       8,  12,  16,  24,  33,   44, ...
%e A218340        7,     14,      77,      79, 154, 158, 553, 869, 1106, ...
%e A218340        5,     10,      15,      20,  30,  32,  40,  53,   55, ...
%e A218340   292561, 585122, 3218171, 6436342;
%e A218340   ...
%p A218340 with(numtheory):
%p A218340 M:= proc(n) M(n):= divisors(23^n-1) minus U(n-1) end:
%p A218340 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218340 T:= n-> sort([M(n)[]])[]:
%p A218340 seq(T(n), n=1..5);
%t A218340 M[n_] := M[n] = Divisors[23^n-1] ~Complement~ U[n-1];
%t A218340 U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t A218340 T[n_] := Sort[M[n]];
%t A218340 Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y A218340 Column k=9 of A212737.
%Y A218340 Column k=1 gives: A218363.
%Y A218340 Row lengths are A212957(n,23).
%K A218340 nonn,tabf,look
%O A218340 1,2
%A A218340 _Alois P. Heinz_, Oct 26 2012