A063695 Remove even-positioned bits from the binary expansion of n.

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

Comments

In the base 4 expansion of n, change 1 to 0 and 3 to 2. - Paolo Xausa, Feb 27 2025

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Ralf Stephan, Some divide-and-conquer sequences ...

Ralf Stephan, Table of generating functions

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

a(n) = 2*(n - A380110(n)). - Paolo Xausa, Feb 27 2025

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.

Mathematica

A063695[n_] := FromDigits[ReplaceAll[IntegerDigits[n, 4], {1 -> 0, 3 -> 2}], 4];
Array[A063695, 100, 0] (* Paolo Xausa, Feb 27 2025 *)

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

Adjacent sequences: A063692 A063693 A063694 * A063696 A063697 A063698

Keyword

nonn,base,easy,changed

Author

Antti Karttunen, Aug 03 2001

Status

approved