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A218339
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Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(19) listed in ascending order.
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4
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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) = {}.
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EXAMPLE
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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, ...
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MAPLE
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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);
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MATHEMATICA
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M[n_] := M[n] = Divisors[19^n-1] ~Complement~ U[n-1];
U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
T[n_] := Sort[M[n]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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