A212529 Negative numbers in base -2.

11, 10, 1101, 1100, 1111, 1110, 1001, 1000, 1011, 1010, 110101, 110100, 110111, 110110, 110001, 110000, 110011, 110010, 111101, 111100, 111111, 111110, 111001, 111000, 111011, 111010, 100101, 100100, 100111, 100110, 100001, 100000, 100011, 100010, 101101, 101100, 101111, 101110, 101001, 101000, 101011, 101010, 11010101

Offset

1,1

Comments

The formula a(n) = A039724(-n) is slightly misleading because sequence A039724 isn't defined for n < 0, and none of the terms a(n) is a term of A039724. It can be seen as the definition of the extension of A039724 to negative indices. Also, recursive definitions or implementations of A039724 require that function to be defined for negative arguments, and using a generic formula it will work as expected for -n, n > 0. - M. F. Hasler, Oct 18 2018

Links

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

Joerg Arndt, Matters Computational (The Fxtbook), pp. 58-59.

Formula

a(n) = A039724(-n). - Reinhard Zumkeller, Feb 05 2014

Maple

a:= proc(n) local d, i, l, m;
      m:= n; l:= NULL;
      for i from 0 while m>0 do
        d:= irem(m, 2, 'm');
        if d=1 and irem(i, 2)=0 then m:= m+1 fi;
        l:= d, l
      od; parse(cat(l))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 20 2012

Mathematica

negabin[n_] := negabin[n] = If[n == 0, 0, negabin[Quotient[n - 1, -2]]*10 + Mod[n, 2]]; a[n_] := negabin[-n]; Array[a, 50] (* Amiram Eldar, Jul 23 2023 *)

Prog

(Haskell)
a212529 = a039724 . negate  -- Reinhard Zumkeller, Feb 05 2014
(Python)
def A212529(n):
    s, q = '', -n
    while q >= 2 or q < 0:
        q, r = divmod(q, -2)
        if r < 0:
            q += 1
            r += 2
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016
(PARI) A212529(n)=A039724(-n) \\ M. F. Hasler, Oct 16 2018

Crossrefs

Cf. A039724 (nonnegative numbers in base -2).

Cf. A007608 (nonnegative numbers in base -4), A212526 (negative numbers in base -4).

Cf. A005352.

Sequence in context: A364121 A038324 A164125 * A004289 A360494 A287710

Adjacent sequences: A212526 A212527 A212528 * A212530 A212531 A212532

Keyword

nonn,base

Author

Joerg Arndt, May 20 2012

Status

approved