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a(n) = 10^n - (5^(2^n) mod 10^n).
7

%I #15 Apr 24 2017 18:25:46

%S 5,75,375,9375,9375,109375,7109375,87109375,787109375,1787109375,

%T 81787109375,81787109375,81787109375,40081787109375,740081787109375,

%U 3740081787109375,43740081787109375,743740081787109375

%N a(n) = 10^n - (5^(2^n) mod 10^n).

%C a(n)^3 mod 10^n = a(n).

%C a(n) is the unique positive integer less than 10^n such that a(n) is divisible by 5^n and a(n) + 1 is divisible by 2^n. - _Eric M. Schmidt_, Sep 01 2012

%C a(n+1) + a(n)^2 == 0 (mod 10^(n+1)). - _Robert Israel_, Apr 24 2017

%H Robert Israel, <a href="/A216093/b216093.txt">Table of n, a(n) for n = 1..999</a>

%F 2^(4*5^(n-1)) mod 10^n - 1.

%p f:= n -> (-5 &^(2^n) mod 10^n):

%p map(f, [$1..30]); # _Robert Israel_, Apr 24 2017

%o (Sage) def A216093(n) : return crt(-1, 0, 2^n, 5^n) # _Eric M. Schmidt_, Sep 01 2012

%Y Cf. A007185, A016090, A216092, A091663, A018248.

%K nonn

%O 1,1

%A _V. Raman_, Sep 01 2012