A070883 Bitwise XOR of n and n-th prime.

3, 1, 6, 3, 14, 11, 22, 27, 30, 23, 20, 41, 36, 37, 32, 37, 42, 47, 80, 83, 92, 89, 68, 65, 120, 127, 124, 119, 112, 111, 96, 163, 168, 169, 182, 179, 184, 133, 128, 133, 154, 159, 148, 237, 232, 233, 252, 239, 210, 215, 218, 219, 196, 205, 310, 319, 308, 309, 302

Offset: 1

Author

Reinhard Zumkeller, May 22 2002

Keywords

• nonn
• look

Comments

For any integer k, XOR(n,k) = 2*OR(n,k) - (n+k). - Gary Detlefs, Oct 26 2013

Examples

			A000040(25)=97, [25]2 = '00011001', [97]2 = '01100001' '00011001' XOR '01100001' = '01111000', therefore a(25)=120.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, aut.
• Eric Weisstein's World of Mathematics, XOR.

Crossrefs

Cf. A169810, A169811, A194187.

Cf. A265885 (IMPL).

Programs

Haskell

import Data.Bits (xor)
a070883 n = a070883_list !! (n-1)
a070883_list = zipWith xor [1..] a000040_list
-- Reinhard Zumkeller, Jun 23 2015

Mathematica

Table[ BitXor[ n, Prime[n]], {n, 1, 55}]

PARI

a(n) = bitxor(n, prime(n));

Python

from sympy import prime
def a(n): return n^prime(n)
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Mar 05 2022

Formula

a(n) = 2*OR(p,n) - (p+n), for n-th prime p. - Gary Detlefs, Oct 26 2013