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Irregular triangle whose rows are all finite sequences of positive integers that are polydivisible and strictly pandigital.
3

%I #8 Jun 09 2018 08:43:01

%S 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,

%T 4,7,2,9,3,8,1,6,5,4,7,2,9,10

%N Irregular triangle whose rows are all finite sequences of positive integers that are polydivisible and strictly pandigital.

%C 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.

%D Matt Parker, Things to make and do in the fourth dimension, 2015, pages 7-9.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>

%e Triangle is:

%e {1}

%e {1,2}

%e {1,2,3}

%e {3,2,1}

%e {1,2,3,6,5,4}

%e {3,2,1,6,5,4}

%e {3,8,1,6,5,4,7,2}

%e {3,8,1,6,5,4,7,2,9}

%e {3,8,1,6,5,4,7,2,9,10}

%t polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q,k]],k],{k,Length[q]}];

%t Flatten[Table[Select[Permutations[Range[n]],polyQ],{n,8}]]

%Y Cf. A000670, A010784, A030299, A050289, A143671, A144688, A156069, A156071, A158242, A163574, A240763, A305701, A305712, A305714 (row lengths).

%K base,fini,tabf,full,nonn

%O 1,3

%A _Gus Wiseman_, Jun 08 2018