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%I #30 Jan 14 2021 21:17:05
%S 9,96,972,9936,98000,990000,9702000,90000000,810000000,9810000000,
%T 73810000000,900000000000,0,0,900000000000000,9900000000000000,
%U 28900000000000000,0,0,90000000000000000000,0,0,0,900000000000000000000000
%N The largest n-digit number whose last k digits are divisible by k^2 for k = 1..n, otherwise 0.
%C a(13)=0, a(14)=0 because there are no 13- or 14-digit numbers which satisfy the requirements. The sequence is infinite.
%H Shyam Sunder Gupta, <a href="/A228011/b228011.txt">Table of n, a(n) for n = 1..150</a>
%e There are ten one-digit numbers divisible by 1 and largest is 9 so a(1)=9.
%e For two-digit numbers, the second digit must make it divisible by 2^2, which gives 96 as the largest to satisfy the requirement, so a(2)=96.
%t a = Table[j, {j, 0, 9}]; r = 2; s2 = 10; t = a; xs = {Last[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, Last[s]], xs = Append[xs, 0]]]; s2 = s1; a = b; r++]; xs
%Y Cf. A079238.
%K nonn,base
%O 1,1
%A _Shyam Sunder Gupta_, Aug 08 2013
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