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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

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OFFSET

0,5

COMMENTS

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

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

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

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(Haskell)

import Data.Bits ((.&.), (.|.))

a086099 n = foldl1 (.|.) $ zipWith (.&.) [0..] $ reverse [0..n] :: Integer

-- Reinhard Zumkeller, Jun 04 2012

(PARI) a(n) = n++; 1<<logint(n, 2) - 1<<valuation(n, 2); \\ Kevin Ryde, Apr 11 2023

CROSSREFS

Cf. A003817 (even bisection), A062383.

Cf. A086100 (in binary), A007088.

Cf. A053644, A006519.