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%I #16 Jul 09 2019 13:12:08
%S 11,108,1515,12195,102564,11415525,108108108,1219512195,1219512195,
%T 102564102564,102564102564,1012658227848,121951219512195,
%U 161290322580645,1176470588235294,101214574898785425
%N Smallest number not divisible by 10 such that if inserted into itself generates at least n different multiples.
%C Multiples of 10 are excluded otherwise the sequence would be equal to A011557, for n>0.
%C a(6) = 11415525 is the first case where the digits of a(n) are more than n+1.
%C A011557(n) < a(n) <= 15*A094028(n-2) that is 10^n < a(n) <= 5*(100^(n-1)-1)/33, for n>2. - _Giovanni Resta_, Jul 04 2019
%C Here a(8) = a(9) and a(10) = a(11). If we would ask for "exactly" n different multiples then a(8) = 2032520325 and a(10) = 103896103896. - _Giovanni Resta_, Jul 04 2019
%e a(1) = 11 because 1111/11 = 101;
%e a(2) = 108 because 110808/108 = 1026 and 101088/108 = 936;
%e a(5) = 102564 because 110256402564/102564 = 1075001, 101025642564/102564 = 985001, 102102564564/102564 = 995501, 102510256464/102564 = 999476, 102561025644/102564 = 999971.
%p P:=proc(q) local a,b,i,j,n,t: for j from 1 to q do
%p for n from 10^j+1 to q do if n mod 10>0 then b:=length(n):
%p t:={}: for i from 1 to b-1 do
%p a:=((trunc(n/10^i)*10^b+n)*10^i+(n mod 10^i))/n:
%p if frac(a)=0 then t:=t union {a}: fi: od:
%p if nops(t)>=j then print(n); break: fi: fi: od: od: end: P(10^9);
%Y Cf. A011557, A094028.
%K base,nonn,more
%O 1,1
%A _Paolo P. Lava_, Jul 03 2019
%E a(9)-a(16) from _Giovanni Resta_, Jul 04 2019
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