Number Theory > Arithmetic > Number Bases v

Negadecimal

The negadecimal representation of a number n is given by the coefficients in


where , 1, ..., 9. The following table gives the negadecimal representations for the first few integers (A039723).

n negadecimal n negadecimal n 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, ... (Sloane's A051022).

 

Decimal, Negabinary




References

Sloane, N. J. A. Sequences A039723 and A051022 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/.