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A082399 a(1) = 1; thereafter, a(n) is the smallest nonnegative number such that the number Sum_{i=1..n} a(i)*10^(n-i) is divisible by n.

%I A082399 #9 May 26 2013 15:07:12
%S A082399 1,0,2,0,0,0,5,6,4,0,5,10,2,2,5,6,16,8,14,0,7,18,19,2,5,10,6,0,25,20,
%T A082399 2,20,17,12,20,28,13,4,13,30,16,20,36,4,35,28,28,16,29,10,39,14,12,4,
%U A082399 50,20,14,24,7,50,14,54,55,18,10,44,62,52,63,50,7,18,6,62,55,54,54,54,35,10
%N A082399 a(1) = 1; thereafter, a(n) is the smallest nonnegative number such that the number Sum_{i=1..n} a(i)*10^(n-i) is divisible by n.
%C A082399 Suggested by studying A144688. If all a(n) had turned out to be in the range 0 to 9 then this sequence would have produced a counterexample to the assertion that A144688 is finite.
%C A082399 The old entry with this A-number was a duplicate of A080825.
%H A082399 Paul Tek, <a href="/A082399/b082399.txt">Table of n, a(n) for n = 1..10000</a>
%e A082399 After we have the first 11 terms, 1,0,2,0,0,0,5,6,4,0,5, the next number x must be chosen so that 102000564050 + x is divisible by 12; this implies that x = 10.
%p A082399 M:=80; a[1]:=1; N:=1;
%p A082399 for n from 2 to M do
%p A082399 N:=10*N; t2:=N mod n;
%p A082399 if t2 = 0 then a[n]:=0; else a[n]:=n-t2; fi;
%p A082399 N:=N+a[n]; od: [seq(a[n],n=1..M)];
%Y A082399 See A051883 for another version. Cf. A144688.
%K A082399 nonn
%O A082399 1,3
%A A082399 _N. J. A. Sloane_, Feb 08 2009