A228013 The smallest n-digit number whose last k digits are divisible by k^2 for k = 1..n, otherwise 0 (for n > 1).

0, 12, 108, 1072, 10000, 108000, 1666000, 10000000, 810000000, 1000000000, 73810000000, 873810000000, 0, 0, 900000000000000, 1000000000000000, 28900000000000000, 0, 0, 10000000000000000000, 0, 0, 0, 900000000000000000000000

Offset

1,2

Comments

a(13)=0, a(14)=0 because there are no 13- or 14-digit numbers which satisfy the requirements. The sequence is infinite.

Links

Shyam Sunder Gupta, Table of n, a(n) for n = 1..150

Example

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.

Mathematica

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

Crossrefs

Cf. A079238.

Sequence in context: A140317 A069653 A155608 * A225779 A289291 A138432

Adjacent sequences: A228010 A228011 A228012 * A228014 A228015 A228016

Keyword

nonn,base

Author

Shyam Sunder Gupta, Aug 08 2013

Status

approved