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=> Algebraic Integer
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=> Goodstein Sequence
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=> Negabinary
=> Negadecimal
=> Nialpdrome
=> Nonregular Number
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=> One-Seventh Ellipse
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=> Repeating Decimal
=> Saunders Graphic
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=> Vigesimal
Ziyaretçi defteri
 

Negadecimal

The negadecimal representation of a number n is its representation in base -10 (i.e., base negative 10). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in

n = sum_(i=0)a_i(-10)^i
(1)
= ...+a_2(-10)^2+a_1(-10)^1+a_0(-10)^0,
(2)

where a_i=0, 1, ..., 9.

The negadecimal digits may be obtained with the Mathematica 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).

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).


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