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

1,1

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).

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A279242 A094095 A187882 * A074675 A235155 A167841

Adjacent sequences: A212539 A212540 A212541 * A212543 A212544 A212545

Keyword

base,nonn

Author

Joerg Arndt, May 20 2012

Status

approved