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
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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
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Select[Range[0,10000],Union[IntegerDigits[#]]==Range[0,Max[IntegerDigits[#]]]&]
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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
- Matt Parker, Things to make and do in the fourth dimension, 2015, pages 7-9.
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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
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}
- Matt Parker, Things to make and do in the fourth dimension, 2015, pages 7-9.
Cf.
A000670,
A010784,
A030299,
A050289,
A143671,
A144688,
A156069,
A156071,
A158242,
A163574,
A240763,
A305701,
A305712,
A305714 (row lengths).
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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
8 = 2 * 4.
81 = 3 * 27.
816 = 4 * 204.
8165 = 5 * 1633.
81654 = 6 * 13609.
816543 = 7 * 116649.
8165432 = 8 * 1020679.
81654327 = 9 * 9072703.
Showing 1-4 of 4 results.
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