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A199398 XOR of the first n odd numbers. 2
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

CROSSREFS

Cf. A126084 (XOR of first n primes).

Sequence in context: A196833 A245224 A016638 * A296453 A011294 A282072

Adjacent sequences:  A199395 A199396 A199397 * A199399 A199400 A199401

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Nov 05 2011

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.