|
|
A218336
|
|
Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(11) listed in ascending order.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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]];
|
|
CROSSREFS
|
Last elements of rows give: A024127.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|