A199398 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A126084 (XOR of first n primes).

Sequence in context: A196833 A245224 A016638 * A296453 A081544 A011294

Adjacent sequences: A199395 A199396 A199397 * A199399 A199400 A199401

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Nov 05 2011

STATUS

approved