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

1, 2, 4, 8, 16, 3, 6, 9, 12, 18, 24, 32, 36, 48, 72, 96, 144, 288, 307, 614, 1228, 2456, 4912, 5, 10, 15, 20, 29, 30, 40, 45, 58, 60, 64, 80, 87, 90, 116, 120, 145, 160, 174, 180, 192, 232, 240, 261, 290, 320, 348, 360, 435, 464, 480, 522, 576, 580, 696, 720

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..19, flattened

Eric Weisstein's World of Mathematics, Irreducible Polynomial

Eric Weisstein's World of Mathematics, Polynomial Order

Formula

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) = {}.

Example

Triangle begins:
      1,      2,      4,      8,      16;
      3,      6,      9,     12,      18,  24, 32, 36, 48, 72, ...
    307,    614,   1228,   2456,    4912;
      5,     10,     15,     20,      29,  30, 40, 45, 58, 60, ...
  88741, 177482, 354964, 709928, 1419856;

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(17^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
T:= n-> sort([M(n)[]])[]:
seq(T(n), n=1..5);

Mathematica

M[n_] := M[n] = Divisors[17^n-1] ~Complement~ U[n-1];
U[n_] := 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 12 2023, after Alois P. Heinz *)

Crossrefs

Column k=7 of A212737.

Column k=1 gives: A218361.

Row lengths are A212957(n,17).

Sequence in context: A102251 A339853 A373944 * A218468 A308539 A036122

Adjacent sequences: A218335 A218336 A218337 * A218339 A218340 A218341

Keyword

nonn,tabf,look

Author

Alois P. Heinz, Oct 26 2012

Status

approved