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a(n) = 2^(2*5^(n-1)) mod 10^n.
5

%I #16 May 21 2021 15:46:40

%S 4,24,624,624,90624,890624,2890624,12890624,212890624,8212890624,

%T 18212890624,918212890624,9918212890624,59918212890624,

%U 259918212890624,6259918212890624,56259918212890624,256259918212890624

%N a(n) = 2^(2*5^(n-1)) 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 2^n and a(n) + 1 is divisible by 5^n. - _Eric M. Schmidt_, Sep 01 2012

%F a(n) = 5^(2^n) mod 10^n - 1.

%t Table[PowerMod[5,2^n,10^n],{n,20}]-1 (* _Harvey P. Dale_, Dec 17 2017 *)

%o (Sage) def A216092(n) : return crt(0, -1, 2^n, 5^n) # _Eric M. Schmidt_, Sep 01 2012

%Y Cf. A007185, A016090, A216093, A091664, A018247.

%K nonn

%O 1,1

%A _V. Raman_, Sep 01 2012