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%I #22 Jan 14 2021 21:16:33
%S 2,21,210,2100,21076,210769,2107694,21076947,210769470,6300846559
%N The smallest n-digit number whose first k digits are divisible by the k-th prime for k = 1..n.
%C There are 10 terms in the series and the 10-digit number 6300846559 is the last number to satisfy the requirements.
%e There are four one-digit numbers divisible by the first prime (2) and the smallest is 2, so a(1)=2.
%e For two-digit numbers, the second digit must make it divisible by 3, which gives 21 as smallest to satisfy the requirement, so a(2)=21.
%t a=Table[j, {j, 2, 8, 2}]; r=2; t={}; While[!a == {}, n=Length[a]; nmin=First[a]; k=1; b={}; While[!k>n, z0=a[[k]]; Do[z=10*z0+j; If[Mod[z, Prime[r]]==0, b=Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmin]; a=b; r++]; t
%Y Subsequence of A079206.
%Y Cf. A143867, A225613.
%K nonn,base,fini,full
%O 1,1
%A _Shyam Sunder Gupta_, Aug 04 2013
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