A229763 -id:A229763 - cp's OEIS frontend

A229762 a(n) = (n XOR floor(n/2)) AND floor(n/2), where AND and XOR are bitwise logical operators.

0, 0, 1, 0, 2, 2, 1, 0, 4, 4, 5, 4, 2, 2, 1, 0, 8, 8, 9, 8, 10, 10, 9, 8, 4, 4, 5, 4, 2, 2, 1, 0, 16, 16, 17, 16, 18, 18, 17, 16, 20, 20, 21, 20, 18, 18, 17, 16, 8, 8, 9, 8, 10, 10, 9, 8, 4, 4, 5, 4, 2, 2, 1, 0, 32, 32, 33, 32, 34, 34, 33, 32, 36, 36, 37, 36, 34, 34, 33

Offset: 0

Alex Ratushnyak, Sep 28 2013

a(n) has a 01 bit pair in place of each 10 bit pair in n, and everywhere else 0 bits. Or equivalently a(n) has a 1-bit immediately below each run of 1's in n, but excluding a run ending at the least significant bit since below that is below the radix point. - Kevin Ryde, Feb 27 2021

			From _Kevin Ryde_, Feb 27 2021: (Start)
     n = 7267 = binary 1110001100011
  a(n) =  528 = binary   01000010000   1-bit below each run
(End)

Reinhard Zumkeller, Table of n, a(n) for n = 0..8191

Cf. A003188 (n XOR floor(n/2)).
Cf. A048724 (n XOR (n*2)).
Cf. A048735 (n AND floor(n/2)).
Cf. A213370 (n AND (n*2)).
Cf. A213064 (n XOR (n*2) AND (n*2), 1-bit above each run).
Cf. A229763 ((2*n) XOR n AND n, low 1-bit each run).

import Data.Bits ((.&.), xor, shiftR)
a229762 n = (n `xor` shiftR n 1) .&. shiftR n 1 :: Int
-- Reinhard Zumkeller, Oct 10 2013

a(n) = bitnegimply(n>>1,n); \\ Kevin Ryde, Feb 27 2021

for n in range(333): print (n ^ (n>>1)) & (n>>1),

def A229762(n): return ~n& n>>1 # Chai Wah Wu, Jun 29 2022

a(n) = (n XOR floor(n/2)) AND floor(n/2) = (n AND floor(n/2)) XOR floor(n/2).

a(n) = floor(n/2) AND NOT n. - Chai Wah Wu, Jun 29 2022

cp's OEIS Frontend

A229762 a(n) = (n XOR floor(n/2)) AND floor(n/2), where AND and XOR are bitwise logical operators.

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