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A212526 Negative integers in base -4.

%I A212526 #26 Apr 10 2016 02:31:14
%S A212526 13,12,11,10,23,22,21,20,33,32,31,30,1303,1302,1301,1300,1313,1312,
%T A212526 1311,1310,1323,1322,1321,1320,1333,1332,1331,1330,1203,1202,1201,
%U A212526 1200,1213,1212,1211,1210,1223,1222,1221,1220
%N A212526 Negative integers in base -4.
%C A212526 Interleaving with zeros gives A212542 (base 2i representation of negative integers).
%C A212526 More precisely, a(n) is the representation of -n in base -4. - _M. F. Hasler_, May 21 2012
%H A212526 Joerg Arndt, <a href="/A212526/b212526.txt">Table of n, a(n) for n = 1..1000</a>
%e A212526 a(13)=1303:  1*(-4)^3 + 3*(-4)^2 + 0*(-4)^1 + 3*(-4)^0 = -64 + 48 +3 = -13.
%p A212526 a:= proc(n) local d, i, l, m;
%p A212526       m:= n;
%p A212526       l:= NULL;
%p A212526       for i from 0 while m>0 do
%p A212526         d:= irem(m, 4, 'm');
%p A212526         if irem (i, 2)=0 and d>0 then d:= 4-d; m:= m+1 fi;
%p A212526         l:= d, l
%p A212526       od; parse(cat(l))
%p A212526     end:
%p A212526 seq(a(n), n=1..60);  # _Alois P. Heinz_, May 20 2012
%o A212526 (PARI) A212526(n,s="")={n=-n;until(!n\=-4,s=Str(n%-4,s));eval(s)}  \\ _M. F. Hasler_, May 21 2012
%o A212526 (Python)
%o A212526 def A212526(n):
%o A212526     s, q = '', -n
%o A212526     while q >= 4 or q < 0:
%o A212526         q, r = divmod(q, -4)
%o A212526         if r < 0:
%o A212526             q += 1
%o A212526             r += 4
%o A212526         s += str(r)
%o A212526     return int(str(q)+s[::-1]) # _Chai Wah Wu_, Apr 10 2016
%Y A212526 Cf. A007608 (Nonnegative integers in base -4).
%K A212526 nonn,base
%O A212526 1,1
%A A212526 _Joerg Arndt_, May 20 2012