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A218339 Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(19) listed in ascending order. 4
1, 2, 3, 6, 9, 18, 4, 5, 8, 10, 12, 15, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360, 27, 54, 127, 254, 381, 762, 1143, 2286, 3429, 6858, 16, 48, 80, 144, 181, 240, 362, 543, 720, 724, 905, 1086, 1448, 1629, 1810, 2172, 2715, 2896, 3258, 3620, 4344, 5430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..18, 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|(19^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,   6,   9,   18;

    4,   5,   8,  10,  12,   15,   20,   24,   30,   36,   40, ...

   27,  54, 127, 254, 381,  762, 1143, 2286, 3429, 6858;

   16,  48,  80, 144, 181,  240,  362,  543,  720,  724,  905, ...

  151, 302, 453, 906, 911, 1359, 1822, 2718, 2733, 5466, 8199, ...

MAPLE

with(numtheory):

M:= proc(n) M(n):= divisors(19^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);

CROSSREFS

Column k=8 of A212737.

Column k=1 gives: A218362.

Row lengths are A212957(n,19).

Sequence in context: A095090 A061947 A018251 * A329248 A276076 A276086

Adjacent sequences:  A218336 A218337 A218338 * A218340 A218341 A218342

KEYWORD

nonn,tabf,look

AUTHOR

Alois P. Heinz, Oct 26 2012

STATUS

approved

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Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)