The negadecimal representation of a number is its representation in base (i.e., base negative 10). It is therefore given by the coefficients in
(1)
| |||
(2)
|
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).
negadecimal | negadecimal | negadecimal | |||
1 | 1 | 11 | 191 | 21 | 181 |
2 | 2 | 12 | 192 | 22 | 182 |
3 | 3 | 13 | 193 | 23 | 183 |
4 | 4 | 14 | 194 | 24 | 184 |
5 | 5 | 15 | 195 | 25 | 185 |
6 | 6 | 16 | 196 | 26 | 186 |
7 | 7 | 17 | 197 | 27 | 187 |
8 | 8 | 18 | 198 | 28 | 188 |
9 | 9 | 19 | 199 | 29 | 189 |
10 | 190 | 20 | 180 | 30 | 170 |
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).