cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Gus Wiseman, Jun 08 2018

Keywords

Crossrefs

Programs

  • Maple
    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
  • Mathematica
    Select[Range[0,10000],Union[IntegerDigits[#]]==Range[0,Max[IntegerDigits[#]]]&]
  • PARI
    isok(n) = if (n==0, return (1)); my(d=Set(digits(n))); (vecmin(d) == 0) && (vecmax(d) == #d - 1); \\ Michel Marcus, Jul 05 2018

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

Views

Author

Gus Wiseman, Jun 08 2018

Keywords

Comments

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.

References

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

Crossrefs

Programs

  • Mathematica
    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}]]

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

Original entry on oeis.org

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

Views

Author

Gus Wiseman, Jun 08 2018

Keywords

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.

Examples

			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}
		

References

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

Crossrefs

Programs

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

A324016 N-digit substring of 81654327 taken from the left.

Original entry on oeis.org

8, 81, 816, 8165, 81654, 816543, 8165432, 81654327
Offset: 1

Views

Author

Seiichi Manyama, Sep 01 2019

Keywords

Comments

A sequence q of length k is strictly pandigital if it is a permutation of {1,2,...,k}. Consider a strictly pandigital sequence q such that Sum_{i=1..m} 10^(m - i) * q_i is a multiple of m+1 for all 1 <= m <= k. Except for 21 and 81654327, there is no such sequence for k <= 30.

Examples

			8        = 2 * 4.
81       = 3 * 27.
816      = 4 * 204.
8165     = 5 * 1633.
81654    = 6 * 13609.
816543   = 7 * 116649.
8165432  = 8 * 1020679.
81654327 = 9 * 9072703.
		

Crossrefs

Showing 1-4 of 4 results.