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A305712
Polydivisible nonnegative integers whose decimal digits span an initial interval of {0,...,9}.
3
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
0,2
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.
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}]]
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Jun 08 2018
STATUS
approved