A216092 a(n) = 2^(2*5^(n-1)) mod 10^n.

4, 24, 624, 624, 90624, 890624, 2890624, 12890624, 212890624, 8212890624, 18212890624, 918212890624, 9918212890624, 59918212890624, 259918212890624, 6259918212890624, 56259918212890624, 256259918212890624

Offset: 1

Author

V. Raman, Sep 01 2012

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..996

Crossrefs

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

Programs

Maple

f:= n -> 2&^(2*5^(n-1)) mod 10^n:
map(f, [$1..100]); # Robert Israel, Mar 13 2025

Mathematica

Table[PowerMod[5,2^n,10^n],{n,20}]-1 (* Harvey P. Dale, Dec 17 2017 *)

Sage

def A216092(n) : return crt(0, -1, 2^n, 5^n) # Eric M. Schmidt, Sep 01 2012

Formula

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

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

a(n-1) == a(n) (mod 10^(n-1)). - Robert Israel, Mar 13 2025