The negadecimal representation of a number 
is its representation in base 
(i.e., base negative 10). It is therefore
given by the coefficients 
in
where 
,
1, ..., 9.
The negadecimal digits may be obtained with the Wolfram Language code
Negadecimal[0] := {0}
Negadecimal[i_] := Rest @ Reverse @
Mod[NestWhileList[(# - Mod[#, 10])/-10&,
i, # != 0& ], 10]
The following table gives the negadecimal representations for the first few integers (A039723).
The numbers having the same decimal and negadecimal representations are those which are sums of distinct powers of 100: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200, ... (OEIS A051022).
See also
Explore with Wolfram|Alpha
References
Sloane, N. J. A. Sequences A039723 and A051022 in "The On-Line Encyclopedia of Integer Sequences."
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Negadecimal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Negadecimal.html