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.

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, 2, 20, 17, 12, 20, 28, 13, 4, 13, 30, 16, 20, 36, 4, 35, 28, 28, 16, 29, 10, 39, 14, 12, 4, 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

Offset: 1

Author

N. J. A. Sloane, Feb 08 2009

Keywords

• nonn

Comments

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.

The old entry with this A-number was a duplicate of A080825.

Examples

			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.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

See A051883 for another version. Cf. A144688.

Programs

Maple

M:=80; a[1]:=1; N:=1;
for n from 2 to M do
N:=10*N; t2:=N mod n;
if t2 = 0 then a[n]:=0; else a[n]:=n-t2; fi;
N:=N+a[n]; od: [seq(a[n],n=1..M)];