

A228010


The number of ndigit numbers whose last k digits are divisible by k^2 for k = 1..n.


1



10, 22, 25, 63, 45, 50, 11, 9, 1, 18, 1, 2, 0, 0, 1, 18, 1, 0, 0, 9, 0, 0, 0, 1, 18, 1, 0, 0, 0, 1, 0, 9, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 1, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 9, 0, 0, 0, 0
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OFFSET

1,1


COMMENTS

The sequence is infinite.


LINKS



EXAMPLE

There are ten onedigit numbers divisible by 1 so a(1)=10.
For twodigit numbers, the second digit must make it divisible by 2^2, which gives 22 numbers: 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 to satisfy the requirement. So a(2)=22.


MATHEMATICA

a = Table[j, {j, 0, 9}]; r = 2; s2 = 10; t = a; xs = {s2}; 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 < 111, b = Append[b, z]; t = Append[t, z]], {j, 0, 9}]; k++]; s = Union[t]; s1 = Length[s]; If[r < 111, xs = Append[xs, s1  s2]]; s2 = s1; a = b; r++]; xs


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



