login
A268726
Index of the toggled bit between n and A268717(n+1): a(n) = A000523(A003987(n, A268717(1+n))).
4
0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 6, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 7, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0
OFFSET
0,3
COMMENTS
A fractal sequence, because a permutation of A007814. Removing zeros yields A268727(n) = a(n)+1.
FORMULA
a(n) = A007814(1 + A006068(n)).
a(n) = A000523(A003987(n, A268717(1+n))).
a(n) = floor(log_2(n XOR A003188(1 + A006068(n)))).
Other identities:
For all n >= 1, a(A003188(n-1)) = A007814(n).
MATHEMATICA
A003188[n_]:=BitXor[n, Floor[n/2]]; A006068[n_]:=If[n<2, n, Block[{m=A006068[Floor[n/2]]}, 2m + Mod[Mod[n, 2] + Mod[m, 2], 2]]]; A268717[n_]:=If[n<1, 0, A003188[1 + A006068[n - 1]]]; a[n_]:= Floor[Log[2, BitXor[n, A268717[n + 1]]]]; Table[a[n], {n, 0, 200}] (* Indranil Ghosh, Apr 02 2017 *)
PROG
(Scheme) (define (A268726 n) (A000523 (A003987bi n (A268717 (+ 1 n))))) ;; A003987bi implements the bitwise-XOR, defined in A003987.
(PARI) A003188(n) = bitxor(n, n\2);
A006068(n) = if(n<2, n, {my(m = A006068(n\2)); 2*m + (n%2 + m%2)%2});
A268717(n) = if(n<1, 0, A003188(1 + A006068(n - 1)));
for(n=0, 200, print1(logint(bitxor(n, A268717(n + 1)), 2), ", ")) \\ Indranil Ghosh, Apr 02 2017
(Python)
def A003188(n): return n^(n//2)
def A006068(n):
if n<2: return n
else:
m=A006068(n//2)
return 2*m + (n%2 + m%2)%2
def A268717(n): return 0 if n<1 else A003188(1 + A006068(n - 1))
print([int(math.floor(math.log(n^A268717(n + 1), 2))) for n in range(201)]) # Indranil Ghosh, Apr 02 2017
CROSSREFS
One less than A268727.
Cf. also array A268833.
Sequence in context: A309332 A109362 A085246 * A035182 A280720 A245964
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Feb 13 2016
STATUS
approved