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A327571
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Triangle T(n,k) read by rows giving the number of zeroless polydivisible numbers in base n that contains only "k" in the digits with 1 <= k <= n-1.
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2
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1, 2, 2, 1, 3, 1, 2, 2, 4, 2, 1, 2, 1, 2, 1, 4, 4, 4, 4, 6, 4, 1, 2, 1, 2, 1, 3, 1, 2, 2, 4, 2, 2, 4, 2, 2, 1, 3, 1, 4, 1, 3, 1, 4, 1, 2, 2, 6, 2, 2, 6, 2, 2, 6, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4
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graph;
refs;
listen;
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OFFSET
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2,2
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LINKS
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FORMULA
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T(n,1) <= T(n,k).
T(n,2*m) >= 2 for m >= 1.
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EXAMPLE
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n | zeroless polydivisible numbers with all digits the same in base n
--+------------------------------------------------------------------
2 | [1]
3 | [1, 11], [2, 22]
4 | [1], [2, 22, 222], [3]
So T(2,1) = 1, T(3,1) = 2, T(3,2) = 2, T(4,1) = 1, T(4,2) = 3, T(4,3) = 1.
Triangle begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12
-----+------------------------------------
2 | 1;
3 | 2, 2;
4 | 1, 3, 1;
5 | 2, 2, 4, 2;
6 | 1, 2, 1, 2, 1;
7 | 4, 4, 4, 4, 6, 4;
8 | 1, 2, 1, 2, 1, 3, 1;
9 | 2, 2, 4, 2, 2, 4, 2, 2;
10 | 1, 3, 1, 4, 1, 3, 1, 4, 1;
11 | 2, 2, 6, 2, 2, 6, 2, 2, 6, 2;
12 | 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1;
13 | 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4;
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PROG
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(Ruby)
def T(k, n)
s = 0
(0..n - 2).each{|i|
s += k * n ** i
return i if s % (i + 1) > 0
}
n - 1
end
(2..n).map{|i| (1..i - 1).map{|j| T(j, i)}}.flatten
end
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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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