A218341 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(29) listed in ascending order.

1, 2, 4, 7, 14, 28, 3, 5, 6, 8, 10, 12, 15, 20, 21, 24, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840, 13, 26, 52, 67, 91, 134, 182, 268, 364, 469, 871, 938, 1742, 1876, 3484, 6097, 12194, 24388, 16, 48, 80, 112, 240, 336, 421, 560

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..16, 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|(29^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,       7,       14,       28;
:      3,       5,       6,       8,       10,       12,  15, ...
:     13,      26,      52,      67,       91,      134, 182, ...
:     16,      48,      80,     112,      240,      336, 421, ...
: 732541, 1465082, 2930164, 5127787, 10255574, 20511148;

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(29^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[29^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=10 of A212737.

Column k=1 gives: A218364.

Row lengths are A212957(n,29).

Sequence in context: A119267 A144978 A018254 * A018660 A018692 A161713

Adjacent sequences: A218338 A218339 A218340 * A218342 A218343 A218344

Keyword

nonn,tabf,look

Author

Alois P. Heinz, Oct 26 2012

Status

approved