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

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

Author

Gus Wiseman, Jun 08 2018

Keywords

• nonn
• base

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.

Links

• Wikipedia, Polydivisible number

Crossrefs

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

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}]]