A199398 XOR of the first n odd numbers.

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, 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, 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

Offset: 1

Author

Paul D. Hanna, Nov 05 2011

Keywords

• nonn
• easy

Examples

			a(2) = 1 XOR 3 = 2; a(3) = 1 XOR 3 XOR 5 = 7; a(4) = 1 XOR 3 XOR 5 XOR 7 = 0.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A126084 (XOR of first n primes).

Programs

Maple

a := proc(n) local u,b,w,k;
u := 1; w := 1; b := true;
for k from 2 to n do
   u := u + 2;
   w := u + `if`(b, -w, +w);
   b := not b;
od; w end:
seq(a(n), n=1..95); # Peter Luschny, Dec 31 2014

Mathematica

With[{c=Range[1,201,2]},Table[BitXor@@Take[c,n],{n,100}]] (* Harvey P. Dale, Nov 19 2011 *)

PARI

a(n)=if(n==1,1,bitxor(a(n-1),2*n-1))

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

Python

from operator import xor
from functools import reduce
def A199398(n): return reduce(xor,range(1,n<<1,2)) # Chai Wah Wu, Jul 09 2022

Formula

G.f.: x*(1 + 2*x + 6*x^2 - 2*x^3 + x^4)/((1-x^2)*(1-x^4)).