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A007608 Nonnegative integers in base -4.

%I A007608 M0926 #54 Feb 16 2025 08:32:31
%S A007608 0,1,2,3,130,131,132,133,120,121,122,123,110,111,112,113,100,101,102,
%T A007608 103,230,231,232,233,220,221,222,223,210,211,212,213,200,201,202,203,
%U A007608 330,331,332,333,320,321,322,323,310,311,312,313,300,301,302,303,13030
%N A007608 Nonnegative integers in base -4.
%C A007608 The base 2i representation (quater-imaginary representation) of nonnegative integers is obtained by interleaving with zeros, cf. A212494.
%C A007608 More precisely, a(n) is the number n written in base -4; numbers [which represent some nonnegative integer] in base -4 are 0, 1, 2, 3, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, ... (A212556) - _M. F. Hasler_, May 20 2012
%D A007608 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.
%D A007608 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007608 Joerg Arndt, <a href="/A007608/b007608.txt">Table of n, a(n) for n = 0..1000</a>
%H A007608 Matthew Szudzik, <a href="https://web.archive.org/web/20130523133059/http://library.wolfram.com/conferences/devconf99/challenge/">A Mathematica programming contest</a>
%H A007608 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a>
%H A007608 Wikipedia, <a href="https://en.wikipedia.org/wiki/Negative_base">Negative base</a>
%t A007608 ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 4], {n, 0, 55}]
%o A007608 (PARI) A007608(n,s="")={until(!n\=-4,s=Str(n%-4,s));eval(s)}  \\ _M. F. Hasler_, May 20 2012
%o A007608 (Haskell)
%o A007608 a007608 0 = 0
%o A007608 a007608 n = a007608 n' * 10 + m where
%o A007608    (n', m) = if r < 0 then (q + 1, r + 4) else (q, r)
%o A007608              where (q, r) = quotRem n (negate 4)
%o A007608 -- _Reinhard Zumkeller_, Jul 15 2012
%o A007608 (Python)
%o A007608 def A007608(n):
%o A007608     s, q = '', n
%o A007608     while q >= 4 or q < 0:
%o A007608         q, r = divmod(q, -4)
%o A007608         if r < 0:
%o A007608             q += 1
%o A007608             r += 4
%o A007608         s += str(r)
%o A007608     return int(str(q)+s[::-1]) # _Chai Wah Wu_, Apr 09 2016
%Y A007608 Cf. A212556 (sorted), A066323 (sum of digits), A212526 (negative integers in base -4).
%Y A007608 Other bases: A007090, A039724, A073785, A073786, A073787, A073788, A073789, A073790 & A039723.
%K A007608 base,nice,easy,nonn
%O A007608 0,3
%A A007608 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_