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A218340
Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(23) listed in ascending order.
4
1, 2, 11, 22, 3, 4, 6, 8, 12, 16, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528, 7, 14, 77, 79, 154, 158, 553, 869, 1106, 1738, 6083, 12166, 5, 10, 15, 20, 30, 32, 40, 53, 55, 60, 80, 96, 106, 110, 120, 159, 160, 165, 212, 220, 240, 265, 318, 330, 352, 424, 440
OFFSET
1,2
LINKS
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|(23^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
EXAMPLE
Triangle begins:
1, 2, 11, 22;
3, 4, 6, 8, 12, 16, 24, 33, 44, ...
7, 14, 77, 79, 154, 158, 553, 869, 1106, ...
5, 10, 15, 20, 30, 32, 40, 53, 55, ...
292561, 585122, 3218171, 6436342;
...
MAPLE
with(numtheory):
M:= proc(n) M(n):= divisors(23^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[23^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=9 of A212737.
Column k=1 gives: A218363.
Row lengths are A212957(n,23).
Sequence in context: A085652 A111090 A111081 * A018491 A031010 A161708
KEYWORD
nonn,tabf,look
AUTHOR
Alois P. Heinz, Oct 26 2012
STATUS
approved