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A228013
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The smallest n-digit number whose last k digits are divisible by k^2 for k = 1..n, otherwise 0 (for n > 1).
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1
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0, 12, 108, 1072, 10000, 108000, 1666000, 10000000, 810000000, 1000000000, 73810000000, 873810000000, 0, 0, 900000000000000, 1000000000000000, 28900000000000000, 0, 0, 10000000000000000000, 0, 0, 0, 900000000000000000000000
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OFFSET
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1,2
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COMMENTS
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a(13)=0, a(14)=0 because there are no 13- or 14-digit numbers which satisfy the requirements. The sequence is infinite.
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LINKS
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EXAMPLE
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There are ten one-digit numbers divisible by 1 and the smallest is 0 so a(1)=0.
For two-digit numbers, the second digit must make it divisible by 2^2, which gives 12 as the smallest to satisfy the requirement, so a(2)=12.
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MATHEMATICA
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a = Table[j, {j, 0, 9}]; r = 2; s2 = 10; t = a; xs = {First[a]}; While[! a == {} , n = Length[a]; k = 1; b = {}; While[! k > n , z0 = a[[k]]; Do[z = 10^(r - 1)*j + z0; If[Mod[z, r*r] == 0 && r < 25, b = Append[b, z]; t = Append[t, z]], {j, 0, 9}]; k++]; s = Union[t]; s1 = Length[s]; If[r < 25, If[ s1 > s2, xs = Append[xs, s[[s2 + 1]]], xs = Append[xs, 0]]]; s2 = s1; a = b; r++]; xs
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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