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A199398 XOR of the first n odd numbers.

%I A199398 #23 Jul 10 2022 03:56:56
%S A199398 1,2,7,0,9,2,15,0,17,2,23,0,25,2,31,0,33,2,39,0,41,2,47,0,49,2,55,0,
%T A199398 57,2,63,0,65,2,71,0,73,2,79,0,81,2,87,0,89,2,95,0,97,2,103,0,105,2,
%U A199398 111,0,113,2,119,0,121,2,127,0,129,2,135,0,137,2,143,0,145,2,151,0,153,2,159,0,161,2,167,0,169,2,175,0,177,2,183,0,185,2,191
%N A199398 XOR of the first n odd numbers.
%H A199398 Indranil Ghosh, <a href="/A199398/b199398.txt">Table of n, a(n) for n = 1..25000</a>
%F A199398 G.f.: x*(1 + 2*x + 6*x^2 - 2*x^3 + x^4)/((1-x^2)*(1-x^4)).
%e A199398 a(2) = 1 XOR 3 = 2; a(3) = 1 XOR 3 XOR 5 = 7; a(4) = 1 XOR 3 XOR 5 XOR 7 = 0.
%p A199398 a := proc(n) local u,b,w,k;
%p A199398 u := 1; w := 1; b := true;
%p A199398 for k from 2 to n do
%p A199398    u := u + 2;
%p A199398    w := u + `if`(b, -w, +w);
%p A199398    b := not b;
%p A199398 od; w end:
%p A199398 seq(a(n), n=1..95); # _Peter Luschny_, Dec 31 2014
%t A199398 With[{c=Range[1,201,2]},Table[BitXor@@Take[c,n],{n,100}]] (* _Harvey P. Dale_, Nov 19 2011 *)
%o A199398 (PARI) a(n)=if(n==1,1,bitxor(a(n-1),2*n-1))
%o A199398 (PARI) Vec((1 + 2*x + 6*x^2 - 2*x^3 + x^4)/(1-x^2)/(1-x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Dec 31 2014
%o A199398 (Python)
%o A199398 from operator import xor
%o A199398 from functools import reduce
%o A199398 def A199398(n): return reduce(xor,range(1,n<<1,2)) # _Chai Wah Wu_, Jul 09 2022
%Y A199398 Cf. A126084 (XOR of first n primes).
%K A199398 nonn,easy
%O A199398 1,2
%A A199398 _Paul D. Hanna_, Nov 05 2011