A212542 Base 2i representation of negative integers.

103, 102, 101, 100, 203, 202, 201, 200, 303, 302, 301, 300, 1030003, 1030002, 1030001, 1030000, 1030103, 1030102, 1030101, 1030100, 1030203, 1030202, 1030201, 1030200, 1030303, 1030302, 1030301, 1030300, 1020003, 1020002, 1020001, 1020000, 1020103, 1020102, 1020101, 1020100, 1020203, 1020202, 1020201, 1020200, 1020303

Offset: 1

Author

Joerg Arndt, May 20 2012

Keywords

• base
• nonn

Comments

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).

Examples

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

Links

• Joerg Arndt, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Maple

a:= proc(n) local d, i, l, m;
      m:= n; l:= NULL;
      for i from 0 while m>0 do
        d:= irem(m, 4, 'm');
        if irem(i, 2)=0 and d>0 then d:= 4-d; m:= m+1 fi;
        l:= d, 0, l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..60); # Alois P. Heinz, May 20 2012