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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Joerg Arndt, May 20 2012
STATUS
approved