A218337 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(13) listed in ascending order.

1, 2, 3, 4, 6, 12, 7, 8, 14, 21, 24, 28, 42, 56, 84, 168, 9, 18, 36, 61, 122, 183, 244, 366, 549, 732, 1098, 2196, 5, 10, 15, 16, 17, 20, 30, 34, 35, 40, 48, 51, 60, 68, 70, 80, 85, 102, 105, 112, 119, 120, 136, 140, 170, 204, 210, 238, 240, 255, 272, 280, 336

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..20, 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|(13^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.

Example

Triangle begins:
:     1,     2,     3,      4,      6,     12;
:     7,     8,    14,     21,     24,     28,  42,  56,  84, 168;
:     9,    18,    36,     61,    122,    183, 244, 366, 549, ...
:     5,    10,    15,     16,     17,     20,  30,  34,  35, ...
: 30941, 61882, 92823, 123764, 185646, 371292;

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(13^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_] := 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 *)

Crossrefs

Column k=6 of A212737.

Column k=1 gives: A218360.

Row lengths are A212957(n,13).

Sequence in context: A061941 A029505 A185092 * A335993 A018309 A245481

Adjacent sequences: A218334 A218335 A218336 * A218338 A218339 A218340

Keyword

nonn,look,tabf

Author

Alois P. Heinz, Oct 26 2012

Status

approved