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A212542 Base 2i representation of negative integers.

%I A212542 #24 Jan 10 2015 10:07:47
%S A212542 103,102,101,100,203,202,201,200,303,302,301,300,1030003,1030002,
%T A212542 1030001,1030000,1030103,1030102,1030101,1030100,1030203,1030202,
%U A212542 1030201,1030200,1030303,1030302,1030301,1030300,1020003,1020002,1020001,1020000,1020103,1020102,1020101,1020100,1020203,1020202,1020201,1020200,1020303
%N A212542 Base 2i representation of negative integers.
%C A212542 Omitting digits for odd powers of 2i (all 0's for the imaginary parts) (e.g. 1030003 --> 1303) gives A212526 (negative integers in base -4).
%H A212542 Joerg Arndt, <a href="/A212542/b212542.txt">Table of n, a(n) for n = 1..1000</a>
%e A212542 a(13) = 1030003: 1*(2*i)^6 + 0 + 3*(2*i)^4 + 0 + 0 + 0 + 3*(2*i)^0 = -64 + 48 + 3 = -13.
%p A212542 a:= proc(n) local d, i, l, m;
%p A212542       m:= n; l:= NULL;
%p A212542       for i from 0 while m>0 do
%p A212542         d:= irem(m, 4, 'm');
%p A212542         if irem(i, 2)=0 and d>0 then d:= 4-d; m:= m+1 fi;
%p A212542         l:= d, 0, l
%p A212542       od; parse(cat(l))/10
%p A212542     end:
%p A212542 seq(a(n), n=1..60); # _Alois P. Heinz_, May 20 2012
%Y A212542 Cf. A212494 (base 2i representation of nonnegative integers).
%K A212542 base,nonn
%O A212542 1,1
%A A212542 _Joerg Arndt_, May 20 2012