A212526 Negative integers in base -4.

13, 12, 11, 10, 23, 22, 21, 20, 33, 32, 31, 30, 1303, 1302, 1301, 1300, 1313, 1312, 1311, 1310, 1323, 1322, 1321, 1320, 1333, 1332, 1331, 1330, 1203, 1202, 1201, 1200, 1213, 1212, 1211, 1210, 1223, 1222, 1221, 1220

Offset: 1

Author

Joerg Arndt, May 20 2012

Keywords

• nonn
• base

Comments

Interleaving with zeros gives A212542 (base 2i representation of negative integers).

More precisely, a(n) is the representation of -n in base -4. - M. F. Hasler, May 21 2012

Examples

			a(13)=1303:  1*(-4)^3 + 3*(-4)^2 + 0*(-4)^1 + 3*(-4)^0 = -64 + 48 +3 = -13.
		

Links

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

Crossrefs

Cf. A007608 (Nonnegative integers in base -4).

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, l
      od; parse(cat(l))
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, May 20 2012

PARI

A212526(n,s="")={n=-n;until(!n\=-4,s=Str(n%-4,s));eval(s)}  \\ M. F. Hasler, May 21 2012

Python

def A212526(n):
    s, q = '', -n
    while q >= 4 or q < 0:
        q, r = divmod(q, -4)
        if r < 0:
            q += 1
            r += 4
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 10 2016