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

%I A182560 #20 May 11 2025 15:26:51
%S A182560 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,
%T A182560 30,31,0,31,32,33,2,35,38,7,32,39,8,41,34,11,46,39,8,47,56,25,42,59,
%U A182560 30,47,56,31,32,57,26,35,62,31,32,63,96,97,34,99,102,39,96,103
%N A182560 a(n) = (a(n-1) AND a(n-2)) XOR n.
%C A182560 Conjecture: sequence contains infinitely many zeros.
%C A182560 a(6*A000695(n)) = 0. [_Reinhard Zumkeller_, May 05 2012]
%H A182560 Reinhard Zumkeller, <a href="/A182560/b182560.txt">Table of n, a(n) for n = 0..10000</a>
%H A182560 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AND.html">AND</a>
%H A182560 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/XOR.html">XOR</a>
%H A182560 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bitwise_operation#AND">Bitwise operation AND</a>
%H A182560 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bitwise_operation#XOR">Bitwise operation XOR</a>
%F A182560 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.
%t A182560 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 *)
%o A182560 (Python)
%o A182560 prpr = 0
%o A182560 prev = 1
%o A182560 for n in range(2,55):
%o A182560    current = (prev & prpr) ^ n
%o A182560    print(prpr, end=' ')
%o A182560    prpr = prev
%o A182560    prev = current
%o A182560 (Haskell)
%o A182560 import Data.Bits ((.&.), xor)
%o A182560 a182560 n = a182560_list !! n
%o A182560 a182560_list = 0 : 1 : 2 : zipWith xor [3..]
%o A182560    (tail $ zipWith (.&.) a182560_list $ tail a182560_list) :: [Integer]
%o A182560 -- _Reinhard Zumkeller_, May 05 2012
%Y A182560 Cf. A182389, A182538.
%K A182560 nonn,base,easy
%O A182560 0,3
%A A182560 _Alex Ratushnyak_, May 05 2012