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A218341 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(29) listed in ascending order.

%I A218341 #23 Feb 18 2025 08:13:29
%S A218341 1,2,4,7,14,28,3,5,6,8,10,12,15,20,21,24,30,35,40,42,56,60,70,84,105,
%T A218341 120,140,168,210,280,420,840,13,26,52,67,91,134,182,268,364,469,871,
%U A218341 938,1742,1876,3484,6097,12194,24388,16,48,80,112,240,336,421,560
%N A218341 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(29) listed in ascending order.
%H A218341 Alois P. Heinz, <a href="/A218341/b218341.txt">Rows n = 1..16, flattened</a>
%H A218341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218341 T(n,k) = k-th smallest element of M(n) = {d : d|(29^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
%e A218341 Triangle begins:
%e A218341        1,       2,       4,       7,       14,       28;
%e A218341        3,       5,       6,       8,       10,       12,  15, ...
%e A218341       13,      26,      52,      67,       91,      134, 182, ...
%e A218341       16,      48,      80,     112,      240,      336, 421, ...
%e A218341   732541, 1465082, 2930164, 5127787, 10255574, 20511148;
%e A218341   ...
%p A218341 with(numtheory):
%p A218341 M:= proc(n) M(n):= divisors(29^n-1) minus U(n-1) end:
%p A218341 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218341 T:= n-> sort([M(n)[]])[]:
%p A218341 seq(T(n), n=1..5);
%t A218341 M[n_] := M[n] = Divisors[29^n-1] ~Complement~ U[n-1];
%t A218341 U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t A218341 T[n_] := Sort[M[n]];
%t A218341 Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y A218341 Column k=10 of A212737.
%Y A218341 Column k=1 gives: A218364.
%Y A218341 Row lengths are A212957(n,29).
%K A218341 nonn,tabf,look
%O A218341 1,2
%A A218341 _Alois P. Heinz_, Oct 26 2012