cp's OEIS Frontend

A218338 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(17) listed in ascending order.

%I A218338 #24 Feb 16 2025 08:33:18
%S A218338 1,2,4,8,16,3,6,9,12,18,24,32,36,48,72,96,144,288,307,614,1228,2456,
%T A218338 4912,5,10,15,20,29,30,40,45,58,60,64,80,87,90,116,120,145,160,174,
%U A218338 180,192,232,240,261,290,320,348,360,435,464,480,522,576,580,696,720
%N A218338 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(17) listed in ascending order.
%H A218338 Alois P. Heinz, <a href="/A218338/b218338.txt">Rows n = 1..19, flattened</a>
%H A218338 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218338 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218338 T(n,k) = k-th smallest element of M(n) = {d : d|(17^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
%e A218338 Triangle begins:
%e A218338       1,      2,      4,      8,      16;
%e A218338       3,      6,      9,     12,      18,  24, 32, 36, 48, 72, ...
%e A218338     307,    614,   1228,   2456,    4912;
%e A218338       5,     10,     15,     20,      29,  30, 40, 45, 58, 60, ...
%e A218338   88741, 177482, 354964, 709928, 1419856;
%p A218338 with(numtheory):
%p A218338 M:= proc(n) M(n):= divisors(17^n-1) minus U(n-1) end:
%p A218338 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218338 T:= n-> sort([M(n)[]])[]:
%p A218338 seq(T(n), n=1..5);
%t A218338 M[n_] := M[n] = Divisors[17^n-1] ~Complement~ U[n-1];
%t A218338 U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t A218338 T[n_] := Sort[M[n]];
%t A218338 Table[T[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y A218338 Column k=7 of A212737.
%Y A218338 Column k=1 gives: A218361.
%Y A218338 Row lengths are A212957(n,17).
%K A218338 nonn,tabf,look
%O A218338 1,2
%A A218338 _Alois P. Heinz_, Oct 26 2012