A086099 a(n) = OR(k AND (n-k): 0<=k<=n), AND and OR bitwise.

0, 0, 1, 0, 3, 2, 3, 0, 7, 6, 7, 4, 7, 6, 7, 0, 15, 14, 15, 12, 15, 14, 15, 8, 15, 14, 15, 12, 15, 14, 15, 0, 31, 30, 31, 28, 31, 30, 31, 24, 31, 30, 31, 28, 31, 30, 31, 16, 31, 30, 31, 28, 31, 30, 31, 24, 31, 30, 31, 28, 31, 30, 31, 0, 63, 62, 63, 60, 63, 62, 63, 56, 63, 62

Offset: 0

Author

Reinhard Zumkeller, Jul 09 2003

Keywords

• nonn
• nice
• easy
• hear
• look

Comments

a(2^n - 1) = 0, a(3*2^n - 1) = 2^n;

A086100(n) = A007088(a(n)).

Examples

			a(4) = (0 AND 4) OR (1 AND 3) OR (2 AND 2) OR (3 AND 1) OR (4 AND 0) -> (000 AND 100) OR (001 AND 011) OR (010 AND 010) OR (011 AND 001) OR (111 AND 000) = 000 OR 011 OR 010 OR 011 OR 000 = 011 -> a(4)=3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, AND
• Eric Weisstein's World of Mathematics, OR
• Reinhard Zumkeller, Logical Convolutions

Crossrefs

Cf. A003817 (even bisection), A062383.

Cf. A086100 (in binary), A007088.

Cf. A053644, A006519.

Cf. A000004, A142149, A142150, A142151, A001477.

Programs

Haskell

import Data.Bits ((.&.), (.|.))
a086099 n = foldl1 (.|.) $ zipWith (.&.) [0..] $ reverse [0..n] :: Integer
-- Reinhard Zumkeller, Jun 04 2012

Mathematica

a[n_] := BitOr @@ Table[BitAnd[k, n - k], {k, 0, n}]; Table[a[n], {n, 0, 73}] (* Jean-François Alcover, Jun 19 2012 *)

PARI

a(n) = n++; 1<Kevin Ryde, Apr 11 2023

Formula

a(2*n) = 2*2^floor(log_2(n)) - 1 = A003817(n).

a(2*n+1) = 2*a(n).

a(n) = A053644(n+1) - A006519(n+1). - Ridouane Oudra, Apr 09 2023