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A218337
Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(13) listed in ascending order.
4
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
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
KEYWORD
nonn,look,tabf
AUTHOR
Alois P. Heinz, Oct 26 2012
STATUS
approved