A218337 - OEIS

%I #24 Mar 30 2016 15:17:23

%S 1,2,3,4,6,12,7,8,14,21,24,28,42,56,84,168,9,18,36,61,122,183,244,366,

%T 549,732,1098,2196,5,10,15,16,17,20,30,34,35,40,48,51,60,68,70,80,85,

%U 102,105,112,119,120,136,140,170,204,210,238,240,255,272,280,336

%N Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(13) listed in ascending order.

%H Alois P. Heinz, <a href="/A218337/b218337.txt">Rows n = 1..20, 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|(13^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,     3,      4,      6,     12;

%e :     7,     8,    14,     21,     24,     28,  42,  56,  84, 168;

%e :     9,    18,    36,     61,    122,    183, 244, 366, 549, ...

%e :     5,    10,    15,     16,     17,     20,  30,  34,  35, ...

%e : 30941, 61882, 92823, 123764, 185646, 371292;

%p with(numtheory):

%p M:= proc(n) M(n):= divisors(13^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_] := Divisors[13^n-1] ~Complement~ U[n-1]; U[n_] := If[n == 0, {}, M[n] ~Union~  U[n-1]]; T[n_] := Sort[M[n]]; Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 13 2015, after _Alois P. Heinz_ *)

%Y Column k=6 of A212737.

%Y Column k=1 gives: A218360.

%Y Row lengths are A212957(n,13).

%K nonn,look,tabf

%O 1,2

%A _Alois P. Heinz_, Oct 26 2012