A063695 - OEIS

%I #22 Jan 30 2023 09:35:19

%S 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,

%T 10,32,32,34,34,32,32,34,34,40,40,42,42,40,40,42,42,32,32,34,34,32,32,

%U 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

%N Remove even-positioned bits from the binary expansion of n.

%H Reinhard Zumkeller, <a href="/A063695/b063695.txt">Table of n, a(n) for n = 0..10000</a>

%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>

%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>

%F a(n) + A063694(n) = n.

%F a(n) = 2*(floor(n/2)-a(floor(n/2))). - _Vladeta Jovovic_, Feb 23 2003

%F From _Ralf Stephan_, Oct 06 2003: (Start)

%F G.f. 1/(1-x) * Sum_{k>=0} (-2)^k*2t^2/(1-t^2) where t = x^2^k.

%F Members of A004514 written twice.

%F (End)

%F a(n) = 4 * a(floor(n / 4)) + 2 * floor(n mod 4 / 2). - _Reinhard Zumkeller_, Sep 26 2015

%F a(n) = A090569(n+1)-1. - _R. J. Mathar_, Jun 22 2020

%e a(25) = 8 because 25 = 11001 in binary and when we AND this with 1010 we are left with 1000 = 8.

%p [seq(every_other_pos(j,2,1),j=0..120)]; # Function every_other_pos given at A063694.

%o (Haskell)

%o a063695 0 = 0

%o a063695 n = 4 * a063695 n' + 2 * div q 2

%o             where (n', q) = divMod n 4

%o -- _Reinhard Zumkeller_, Sep 26 2015

%o (Python)

%o def A063695(n): return n&((1<<(m:=n.bit_length())+(m&1^1))-1)//3 # _Chai Wah Wu_, Jan 30 2023

%Y Cf. A004514 (bisection), A063694 (remove odd-positioned bits), A090569.

%K nonn,base,easy

%O 0,3

%A _Antti Karttunen_, Aug 03 2001