A305715 -id:A305715 - cp's OEIS frontend

A305701 Nonnegative integers whose decimal digits span an initial interval of {0,...,9}.

0, 10, 100, 101, 102, 110, 120, 201, 210, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1023, 1032, 1100, 1101, 1102, 1110, 1120, 1200, 1201, 1202, 1203, 1210, 1220, 1230, 1302, 1320, 2001, 2010, 2011, 2012, 2013, 2021, 2031, 2100, 2101, 2102, 2103

Offset: 1

Gus Wiseman, Jun 08 2018

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000670, A030299, A050289, A144688, A240763, A305712, A305714, A305715.

filter:= proc(n) local L;
  L:= convert(convert(n,base,10),set);
  L = {$0..max(L)}
end proc:
select(filter, [$0..3000]); # Robert Israel, Jun 10 2018

Select[Range[0,10000],Union[IntegerDigits[#]]==Range[0,Max[IntegerDigits[#]]]&]

isok(n) = if (n==0, return (1)); my(d=Set(digits(n))); (vecmin(d) == 0) && (vecmax(d) == #d - 1); \\ Michel Marcus, Jul 05 2018

A305714 Number of finite sequences of positive integers of length n that are polydivisible and strictly pandigital.

Original entry on oeis.org

1, 1, 1, 2, 0, 0, 2, 0, 1, 1, 1

Offset: 0

Gus Wiseman, Jun 08 2018

A 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.

			Sequence of sets of n-digit numbers that are weakly polydivisible and strictly pandigital is (with A = 10):
  {0}
  {1}
  {12}
  {123,321}
  {}
  {}
  {123654,321654}
  {}
  {38165472}
  {381654729}
  {381654729A}

Cf. A000670, A010784, A030299, A050289, A143671, A144688, A156069, A156071, A158242, A163574, A240763, A305701, A305712, A305715.

A305712 Polydivisible nonnegative integers whose decimal digits span an initial interval of {0,...,9}.

Original entry on oeis.org

0, 10, 102, 120, 201, 1020, 1200, 2012, 10200, 12000, 12320, 20120, 32120, 102000, 120000, 123204, 321204, 1024023, 1200003, 1232042, 1444023, 2220001, 3212041, 10240232, 12000032, 12320424, 14440232, 32125240, 50165432

Offset: 0

Gus Wiseman, Jun 08 2018

A number with decimal digit sequence {q_1, ..., q_k} is polydivisible if Sum_{i = 1...m} 10^(m - i) * q_i is a multiple of m for all 1 <= m <= k.

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

Wikipedia, Polydivisible number

Cf. A000670, A030299, A050289, A144688, A156069, A156071, A240763, A305701, A305714, A305715.

polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q,k]],k],{k,Length[q]}];
normseqs[n_]:=Join@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
Sort[FromDigits/@Join@@Table[Select[normseqs[n]-1,First[#]>0&&polyQ[#]&],{n,8}]]

cp's OEIS Frontend

A305701 Nonnegative integers whose decimal digits span an initial interval of {0,...,9}.

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A305714 Number of finite sequences of positive integers of length n that are polydivisible and strictly pandigital.

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A305712 Polydivisible nonnegative integers whose decimal digits span an initial interval of {0,...,9}.

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Mathematica