OFFSET
1,1
COMMENTS
a(n) is A014577 shifted right twice (the definition here is similar to one of the constructions for A034947). - N. J. A. Sloane, Jul 27 2012
Complement of characteristic function of A060833.
From Tanya Khovanova, Apr 21 2020: (Start)
Suppose you have a deck of cards face down with 2^n cards such that the color pattern corresponds to this sequence: 0 for one color, 1 for the other. Then you proceed in the following manner: transfer to top card to the bottom of the deck, deal the next card, then repeat. The dealt cards will have alternating colors.
Even terms of this sequence alternate: 1, 0, 1, 0 and so on.
Removing even-indexed terms doesn't change the sequence. (End)
FORMULA
For n >= 2, Sum_{k=1..n} a(k) = (n + A037834(n-1))/2.
a(1) = 0, a(4*n+2) = 1, a(4*n+4) = 0, a(2*n+1) = a(n+1) for n >= 0. - A.H.M. Smeets, Jul 27 2018
EXAMPLE
First 3 terms are 0,1,1; therefore, a(4) = a(3+1) = 1 - a(3-1) = 1 - a(2) = 0, a(5) = a(3+2) = 1 - a(3-2) = 1 - a(1) = 1 and the sequence begins 0, 1, 1, 0, 1, ...
PROG
(Python)
def A082410(n):
if n == 1:
return 0
s = bin(n-1)[2:]
m = len(s)
i = s[::-1].find('1')
return 1-int(s[m-i-2]) if m-i-2 >= 0 else 1 # Chai Wah Wu, Apr 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 24 2003
STATUS
approved