A182560 a(n) = (a(n-1) AND a(n-2)) XOR n.

0, 1, 2, 3, 6, 7, 0, 7, 8, 9, 2, 11, 14, 7, 8, 15, 24, 25, 10, 27, 30, 15, 24, 31, 0, 25, 26, 3, 30, 31, 0, 31, 32, 33, 2, 35, 38, 7, 32, 39, 8, 41, 34, 11, 46, 39, 8, 47, 56, 25, 42, 59, 30, 47, 56, 31, 32, 57, 26, 35, 62, 31, 32, 63, 96, 97, 34, 99, 102, 39, 96, 103

Offset: 0

Author

Alex Ratushnyak, May 05 2012

Keywords

• nonn
• base
• easy

Comments

Conjecture: sequence contains infinitely many zeros.

a(6*A000695(n)) = 0. [Reinhard Zumkeller, May 05 2012]

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, XOR
• Wikipedia, Bitwise operation AND
• Wikipedia, Bitwise operation XOR

Crossrefs

Cf. A182389, A182538.

Programs

Haskell

import Data.Bits ((.&.), xor)
a182560 n = a182560_list !! n
a182560_list = 0 : 1 : 2 : zipWith xor [3..]
   (tail $ zipWith (.&.) a182560_list $ tail a182560_list) :: [Integer]
-- Reinhard Zumkeller, May 05 2012

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,BitXor[BitAnd[a,b],n+1]}; NestList[nxt,{1,0,1},80][[All,2]] (* Harvey P. Dale, Jan 01 2019 *)

Python

prpr = 0
prev = 1
for n in range(2,55):
   current = (prev & prpr) ^ n
   print(prpr, end=' ')
   prpr = prev
   prev = current

Formula

a(0)=0, a(1)=1, a(n) = (a(n-1) AND a(n-2)) XOR n, where AND is the bitwise AND operator, XOR is the bitwise exclusive-or operator.