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A212529
Negative numbers in base -2.
10
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
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
KEYWORD
nonn,base
AUTHOR
Joerg Arndt, May 20 2012
STATUS
approved