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

1, 2, 5, 10, 3, 4, 6, 8, 12, 15, 20, 24, 30, 40, 60, 120, 7, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330, 16, 48, 61, 80, 122, 183, 240, 244, 305, 366, 488, 610, 732, 915, 976, 1220, 1464, 1830, 2440, 2928, 3660, 4880, 7320, 14640, 25, 50, 3221, 6442

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..23, 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|(11^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.

Example

Triangle begins:
   1,  2,    5,   10;
   3,  4,    6,    8,    12,    15,    20,     24,  30,  40, ...
   7, 14,   19,   35,    38,    70,    95,    133, 190, 266, ...
  16, 48,   61,   80,   122,   183,   240,    244, 305, 366, ...
  25, 50, 3221, 6442, 16105, 32210, 80525, 161050;
  ...

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(11^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[11^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=5 of A212737.

Last elements of rows give: A024127.

Column k=1 gives: A218359.

Row lengths are A212957(n,11).

Sequence in context: A264784 A306679 A125974 * A059955 A099796 A022831

Adjacent sequences: A218333 A218334 A218335 * A218337 A218338 A218339

Keyword

nonn,look,tabf

Author

Alois P. Heinz, Oct 26 2012

Status

approved