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Base 2i representation of negative integers.
3

%I #24 Jan 10 2015 10:07:47

%S 103,102,101,100,203,202,201,200,303,302,301,300,1030003,1030002,

%T 1030001,1030000,1030103,1030102,1030101,1030100,1030203,1030202,

%U 1030201,1030200,1030303,1030302,1030301,1030300,1020003,1020002,1020001,1020000,1020103,1020102,1020101,1020100,1020203,1020202,1020201,1020200,1020303

%N Base 2i representation of negative integers.

%C 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 Joerg Arndt, <a href="/A212542/b212542.txt">Table of n, a(n) for n = 1..1000</a>

%e a(13) = 1030003: 1*(2*i)^6 + 0 + 3*(2*i)^4 + 0 + 0 + 0 + 3*(2*i)^0 = -64 + 48 + 3 = -13.

%p a:= proc(n) local d, i, l, m;

%p m:= n; l:= NULL;

%p for i from 0 while m>0 do

%p d:= irem(m, 4, 'm');

%p if irem(i, 2)=0 and d>0 then d:= 4-d; m:= m+1 fi;

%p l:= d, 0, l

%p od; parse(cat(l))/10

%p end:

%p seq(a(n), n=1..60); # _Alois P. Heinz_, May 20 2012

%Y Cf. A212494 (base 2i representation of nonnegative integers).

%K base,nonn

%O 1,1

%A _Joerg Arndt_, May 20 2012