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A305715
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Irregular triangle whose rows are all finite sequences of positive integers that are polydivisible and strictly pandigital.
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3
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1, 1, 2, 1, 2, 3, 3, 2, 1, 1, 2, 3, 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 8, 1, 6, 5, 4, 7, 2, 3, 8, 1, 6, 5, 4, 7, 2, 9, 3, 8, 1, 6, 5, 4, 7, 2, 9, 10
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OFFSET
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1,3
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COMMENTS
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A positive integer sequence q of length k is strictly pandigital if it is a permutation of {1,2,...,k}. It is polydivisible if Sum_{i = 1...m} 10^(m - i) * q_i is a multiple of m for all 1 <= m <= k.
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REFERENCES
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Matt Parker, Things to make and do in the fourth dimension, 2015, pages 7-9.
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LINKS
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EXAMPLE
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Triangle is:
{1}
{1,2}
{1,2,3}
{3,2,1}
{1,2,3,6,5,4}
{3,2,1,6,5,4}
{3,8,1,6,5,4,7,2}
{3,8,1,6,5,4,7,2,9}
{3,8,1,6,5,4,7,2,9,10}
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MATHEMATICA
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polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q, k]], k], {k, Length[q]}];
Flatten[Table[Select[Permutations[Range[n]], polyQ], {n, 8}]]
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CROSSREFS
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Cf. A000670, A010784, A030299, A050289, A143671, A144688, A156069, A156071, A158242, A163574, A240763, A305701, A305712, A305714 (row lengths).
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KEYWORD
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base,fini,tabf,full,nonn
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AUTHOR
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STATUS
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approved
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