A305715 Irregular triangle whose rows are all finite sequences of positive integers that are polydivisible and strictly pandigital.

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

Offset

1,3

Comments

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.

References

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

Links

Table of n, a(n) for n=1..48.

Wikipedia, Polydivisible number

Example

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}

Mathematica

polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q, k]], k], {k, Length[q]}];
Flatten[Table[Select[Permutations[Range[n]], polyQ], {n, 8}]]

Crossrefs

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

Sequence in context: A129570 A238385 A215652 * A165014 A358871 A357743

Adjacent sequences: A305712 A305713 A305714 * A305716 A305717 A305718

Keyword

base,fini,tabf,full,nonn

Author

Gus Wiseman, Jun 08 2018

Status

approved