2,3,4,82000 series

2,3,4,82000 is an interesting series because of the interesting properties they possess.
It is interesting because
2 is the smallest number that can be expressed in 1's and 0's in base 2.
3 is the smallest number that can be expressed in 1's and 0's in base 2 and base 3.
4 is the smallest number that can be expressed in 1's and 0's in base 2, base 3 and base 4.
82000 is the smallest number that can be expressed in 1's and 0's in base 2, base 3, base 4 and base 5.

2 in base 2 = 10

3 in base 2 = 11
3 in base 3 = 10

4 in base 2 = 100
4 in base 3 = 11
4 in base 4 = 10

82000 in base 2 = 10100000001010000 =$2^{16}+2^{14}+2^6+2^4$
82000 in base 3 = 11011111001 =  $3^{10}+3^9+3^7+3^6+3^5+3^4+3^3+3^0$
82000 in base 4 = 110001100 =  $4^8+4^7+4^3+4^2$
82000 in base 5 = 10111000 = $5^7+ 5^5+ 5^4+ 5^3$

The next number on the series is still unknown and is an open problem for the researchers to find out.