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a(n) = XOR{k OR (n-k): 0<=k<=n}.
6

%I #19 Jul 01 2022 21:41:32

%S 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,

%T 23,27,18,29,17,31,48,33,51,35,54,37,53,39,60,41,63,43,58,45,57,47,40,

%U 49,43,51,46,53,45,55,36,57,39,59,34,61,33,63,96,65,99,67,102,69,101,71

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

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

%H Reinhard Zumkeller, <a href="/A142149/b142149.txt">Table of n, a(n) for n = 0..10000</a>

%H Reinhard Zumkeller, <a href="/A142149/a142149.txt">Logical Convolutions</a>

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

%o (Haskell)

%o import Data.Bits (xor, (.|.))

%o a142149 :: Integer -> Integer

%o a142149 = foldl xor 0 . zipWith (.|.) [0..] . reverse . enumFromTo 1

%o -- _Reinhard Zumkeller_, Mar 31 2015

%o (Python)

%o def A142149(n): return n if n&1 else (n^ n>>1) # _Chai Wah Wu_, Jun 29 2022

%o (PARI) a(n)=if(n%2, n, bitxor(n, n/2)) \\ _Charles R Greathouse IV_, Jul 01 2022

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

%K nonn,hear,look,easy

%O 0,3

%A _Reinhard Zumkeller_, Jul 15 2008