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A063695
Remove even-positioned bits from the binary expansion of n.
10
0, 0, 2, 2, 0, 0, 2, 2, 8, 8, 10, 10, 8, 8, 10, 10, 0, 0, 2, 2, 0, 0, 2, 2, 8, 8, 10, 10, 8, 8, 10, 10, 32, 32, 34, 34, 32, 32, 34, 34, 40, 40, 42, 42, 40, 40, 42, 42, 32, 32, 34, 34, 32, 32, 34, 34, 40, 40, 42, 42, 40, 40, 42, 42, 0, 0, 2, 2, 0, 0, 2, 2, 8, 8, 10, 10, 8, 8, 10, 10, 0, 0
OFFSET
0,3
FORMULA
a(n) + A063694(n) = n.
a(n) = 2*(floor(n/2)-a(floor(n/2))). - Vladeta Jovovic, Feb 23 2003
From Ralf Stephan, Oct 06 2003: (Start)
G.f. 1/(1-x) * Sum_{k>=0} (-2)^k*2t^2/(1-t^2) where t = x^2^k.
Members of A004514 written twice.
(End)
a(n) = 4 * a(floor(n / 4)) + 2 * floor(n mod 4 / 2). - Reinhard Zumkeller, Sep 26 2015
a(n) = A090569(n+1)-1. - R. J. Mathar, Jun 22 2020
EXAMPLE
a(25) = 8 because 25 = 11001 in binary and when we AND this with 1010 we are left with 1000 = 8.
MAPLE
[seq(every_other_pos(j, 2, 1), j=0..120)]; # Function every_other_pos given at A063694.
PROG
(Haskell)
a063695 0 = 0
a063695 n = 4 * a063695 n' + 2 * div q 2
where (n', q) = divMod n 4
-- Reinhard Zumkeller, Sep 26 2015
(Python)
def A063695(n): return n&((1<<(m:=n.bit_length())+(m&1^1))-1)//3 # Chai Wah Wu, Jan 30 2023
CROSSREFS
Cf. A004514 (bisection), A063694 (remove odd-positioned bits), A090569.
Sequence in context: A344834 A344837 A031124 * A081417 A133388 A354643
KEYWORD
nonn,base,easy
AUTHOR
Antti Karttunen, Aug 03 2001
STATUS
approved