A142149 a(n) = XOR{k OR (n-k): 0<=k<=n}.

0, 1, 3, 3, 6, 5, 5, 7, 12, 9, 15, 11, 10, 13, 9, 15, 24, 17, 27, 19, 30, 21, 29, 23, 20, 25, 23, 27, 18, 29, 17, 31, 48, 33, 51, 35, 54, 37, 53, 39, 60, 41, 63, 43, 58, 45, 57, 47, 40, 49, 43, 51, 46, 53, 45, 55, 36, 57, 39, 59, 34, 61, 33, 63, 96, 65, 99, 67, 102, 69, 101, 71

Offset: 0

Author

Reinhard Zumkeller, Jul 15 2008

Keywords

• nonn
• hear
• look
• easy

Comments

a(n) = XOR{k AND (n-k): 0<=k<=n}.

Links

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

Crossrefs

Cf. A003817, A000004, A086099, A142150, A142151, A001477.

Programs

Haskell

import Data.Bits (xor, (.|.))
a142149 :: Integer -> Integer
a142149 = foldl xor 0 . zipWith (.|.) [0..] . reverse . enumFromTo 1
-- Reinhard Zumkeller, Mar 31 2015

PARI

a(n)=if(n%2, n, bitxor(n, n/2)) \\ Charles R Greathouse IV, Jul 01 2022

Python

def A142149(n): return n if n&1 else (n^ n>>1) # Chai Wah Wu, Jun 29 2022

Formula

a(2*n) = A048724(n) and a(2*n+1) = A005408(n).