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A073785 Numbers in base -3.

%I A073785 #25 Feb 16 2025 08:32:46
%S A073785 0,1,2,120,121,122,110,111,112,100,101,102,220,221,222,210,211,212,
%T A073785 200,201,202,12020,12021,12022,12010,12011,12012,12000,12001,12002,
%U A073785 12120,12121,12122,12110,12111,12112,12100,12101,12102,12220,12221,12222
%N A073785 Numbers in base -3.
%D A073785 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.
%H A073785 Reinhard Zumkeller, <a href="/A073785/b073785.txt">Table of n, a(n) for n = 0..10000</a>
%H A073785 Jaime Rangel-Mondragon, <a href="http://demonstrations.wolfram.com/NegabinaryNumbersToDecimal/">Negabinary Numbers to Decimal</a>
%H A073785 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a>
%H A073785 Wikipedia, <a href="http://en.wikipedia.org/wiki/Negative_base">Negative base</a>
%t A073785 ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 3], {n, 0, 45}]
%o A073785 (Haskell)
%o A073785 a073785 0 = 0
%o A073785 a073785 n = a073785 n' * 10 + m where
%o A073785    (n', m) = if r < 0 then (q + 1, r + 3) else (q, r)
%o A073785              where (q, r) = quotRem n (negate 3)
%o A073785 -- _Reinhard Zumkeller_, Jul 07 2012
%o A073785 (Python)
%o A073785 def A073785(n):
%o A073785     s, q = '', n
%o A073785     while q >= 3 or q < 0:
%o A073785         q, r = divmod(q, -3)
%o A073785         if r < 0:
%o A073785             q += 1
%o A073785             r += 3
%o A073785         s += str(r)
%o A073785     return int(str(q)+s[::-1]) # _Chai Wah Wu_, Apr 09 2016
%o A073785 (PARI) A073785 = base(n, b=-3) = if(n, base(n\b, b)*10 + n%b, 0) \\ _Jianing Song_, Oct 20 2018
%Y A073785 Cf. A007089.
%Y A073785 Nonnegative numbers in negative bases: A039723 (b=-10), A039724 (b=-2), this sequence (b=-3), A007608 (b=-4), A073786 (b=-5), A073787 (b=-6), A073788 (b=-7), A073789 (b=-8), A073790 (b=-9).
%Y A073785 Cf. A320636 (negative numbers in base -3).
%K A073785 base,easy,nonn
%O A073785 0,3
%A A073785 _Robert G. Wilson v_, Aug 11 2002