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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 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).

nnegadecimalnnegadecimalnnegadecimal
111119121181
221219222182
331319323183
441419424184
551519525185
661619626186
771719727187
881819828188
991919929189
101902018030170

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

Base, Decimal, Negabinary

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

Negadecimal

Cite this as:

Weisstein, Eric W. "Negadecimal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Negadecimal.html

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