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%I #13 Aug 19 2013 16:53:26
%S 12495360,12573480,12576840,12579360,12597840,12639840,12657480,
%T 12738960,12765840,12789360,12843960,12894360,12957360,12975840,
%U 12978360,13276840,13297840,13567480,13579240,13672480,13675840
%N Eight-digit numbers with all distinct digits with property that the string formed by the last k digits is divisible by k for any 1<=k<=8.
%C There are exactly 921 such numbers with smallest 12495360 and the largest 98765120.
%H Zak Seidov, <a href="/A147749/b147749.txt">Table of n, a(n) for n = 1..921</a> (complete sequence)
%t se8={};Do[If[8-Length@Union@IntegerDigits[n]==Mod[Mod[n,10^3],24]== Mod[Mod[n,10^6],6]==Mod[Mod[n,10^7],7]==0, AppendTo[se8,n]],{n,10000020,99999999,20}];se8
%t Sort[FromDigits/@Select[Select[Flatten[Permutations/@Subsets[Range[0,9],{8}],1],First[#]>0&],And@@Table[Divisible[FromDigits[Take[#,-i]],i],{i,8}]&]] (* _Harvey P. Dale_, Aug 19 2013 *)
%Y A140501, A147636, A147637, A147647.
%K nonn,base,fini,full
%O 1,1
%A _Zak Seidov_, Nov 11 2008