A156071
Concatenation chain arising in A156069.
Original entry on oeis.org
3, 38, 381, 3816, 38165, 381654, 3816547, 38165472, 381654729
Offset: 1
- Matt Parker, Things to make and do in the fourth dimension, 2015, pages 7-9.
A214437
Least numbers whose groups of 2,3,...,n digits taken from the left are divisible by 2,3,...,n.
Original entry on oeis.org
1, 10, 102, 1020, 10200, 102000, 1020005, 10200056, 102000564, 1020005640, 10200056405, 102006162060, 1020061620604, 10200616206046, 102006162060465, 1020061620604656, 10200616206046568, 108054801036000018, 1080548010360000180, 10805480103600001800
Offset: 1
a(6) = 102000 because 10, 102, 1020, 10200 and 102000 are divisible by 2, 3, 4, 5 and 6.
There are nine one-digit numbers that are divisible by 1; the smallest is 1, so a(1)=1.
For two-digit numbers, the second digit must be even, i.e., 0,2,4,6,8 to make it divisible by 2, which gives 10 as the smallest number to satisfy the requirement, so a(2)=10. - _Shyam Sunder Gupta_, Aug 04 2013
-
a=Table[j, {j, 9}]; r=2; t={};
While[!a == {}, n=Length[a]; nmin=Last[a]; k=1; b={};
While[!k>n, z0=a[[k]]; Do[z=10*z0+j; If[Mod[z, r]==0, b=Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmin]; a=b; r++]; t (* Shyam Sunder Gupta, Aug 04 2013 *)
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
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.
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).
-
polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q,k]],k],{k,Length[q]}];
Flatten[Table[Select[Permutations[Range[n]],polyQ],{n,8}]]
A158240
Smallest number made up of n consecutive digits such that every k-digit substring (k <= n) taken from the left is divisible by k (k=1..n).
Original entry on oeis.org
1, 10, 102, 3452, 24365, 123654, 7836542, 38165472, 381654720, 3816547290
Offset: 1
123654, for instance, is in the sequence because 1|1, 2|12, 3|123, 4|1236, 5|12365, 6|123654.
a(4), a(5), a(7), a(9) corrected by
Ray Chandler, Mar 21 2009
A331475
a(n) is the smallest n-digit number using each digit 0 to n-1 once, such that the numbers formed by its last k digits are divisible by k, (k = 1..n).
Original entry on oeis.org
0, 10, 102, 3012, 13240, 123540, 3516240, 16453720, 123567480, 9123567480
Offset: 1
a(3) = 3012 because 2, 12, 012, 3012 are divisible by 1, 2, 3, 4 and it is the least such number with distinct digits 0 to 3.
-
ok[n_] := AllTrue[Range@ IntegerLength@ n, Mod[ Mod[n, 10^#], #] == 0 &]; a[n_] := SelectFirst[ FromDigits /@ Permutations[Range[0, n-1]], # >= 10^(n-1) - 1 && ok[#] &]; Array[a, 10] (* Giovanni Resta, May 04 2020 *)
A334537
a(n) is the largest n-digit number using each digit 0 to n-1 once, such that the numbers formed by its last k digits are divisible by k, (k = 1..n).
Original entry on oeis.org
0, 10, 210, 3120, 43120, 543120, 6531420, 76351240, 876351240, 9876351240
Offset: 1
a(4) = 43120 because 0, 20, 120, 3120 and 43120 are divisible by 1, 2, 3, 4 and 5, and it is the largest such number with distinct digits 0 to 4.
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