cp's OEIS Frontend

A218336 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(11) listed in ascending order.

%I A218336 #23 Feb 16 2025 08:33:18
%S A218336 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 A218336 190,266,665,1330,16,48,61,80,122,183,240,244,305,366,488,610,732,915,
%U A218336 976,1220,1464,1830,2440,2928,3660,4880,7320,14640,25,50,3221,6442
%N A218336 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(11) listed in ascending order.
%H A218336 Alois P. Heinz, <a href="/A218336/b218336.txt">Rows n = 1..23, flattened</a>
%H A218336 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218336 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218336 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 A218336 Triangle begins:
%e A218336    1,  2,    5,   10;
%e A218336    3,  4,    6,    8,    12,    15,    20,     24,  30,  40, ...
%e A218336    7, 14,   19,   35,    38,    70,    95,    133, 190, 266, ...
%e A218336   16, 48,   61,   80,   122,   183,   240,    244, 305, 366, ...
%e A218336   25, 50, 3221, 6442, 16105, 32210, 80525, 161050;
%e A218336   ...
%p A218336 with(numtheory):
%p A218336 M:= proc(n) M(n):= divisors(11^n-1) minus U(n-1) end:
%p A218336 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218336 T:= n-> sort([M(n)[]])[]:
%p A218336 seq(T(n), n=1..5);
%t A218336 M[n_] := M[n] = Divisors[11^n - 1] ~Complement~ U[n-1];
%t A218336 U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t A218336 T[n_] := Sort[M[n]];
%t A218336 Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y A218336 Column k=5 of A212737.
%Y A218336 Last elements of rows give: A024127.
%Y A218336 Column k=1 gives: A218359.
%Y A218336 Row lengths are A212957(n,11).
%K A218336 nonn,look,tabf
%O A218336 1,2
%A A218336 _Alois P. Heinz_, Oct 26 2012