A355487 Bitwise XOR of the base-4 digits of n.

0, 1, 2, 3, 1, 0, 3, 2, 2, 3, 0, 1, 3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 3, 2, 1, 0, 2, 3, 0, 1, 2, 3, 0, 1, 3, 2, 1, 0, 0, 1, 2, 3, 1, 0, 3, 2, 3, 2, 1, 0, 2, 3, 0, 1, 1, 0, 3, 2, 0, 1, 2, 3, 1, 0, 3, 2, 0, 1, 2, 3, 3, 2, 1, 0, 2, 3, 0, 1, 0, 1, 2, 3, 1, 0, 3

Offset: 0

Author

Kevin Ryde, Jul 04 2022

Keywords

• nonn
• base
• easy

Comments

Equivalently, the parity of the odd position 1-bits of n and the parity of the even position 1-bits of n, combined as a(n) = 2*A269723(n) + A341389(n).

In GF(2)[x] polynomials encoded as bits of an integer (least significant bit for the constant term), a(n) is remainder n mod x^2 + 1.

Examples

			n=35 has base-4 digits 203 so a(35) = 2 XOR 0 XOR 3 = 1.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A030373 (base 4 digits), A003987 (XOR).

Cf. A341389, A269723, A010060.

Cf. A353167 (indices of 0's).

Other digit operations: A053737 (sum), A309954 (product).

Programs

Mathematica

a[n_] := BitXor @@ IntegerDigits[n, 4]; Array[a, 100, 0] (* Amiram Eldar, Jul 05 2022 *)

PARI

a(n) = if(n==0,0, fold(bitxor,digits(n,4)));

Python

from operator import xor
from functools import reduce
from sympy.ntheory import digits
def a(n): return reduce(xor, digits(n, 4)[1:])
print([a(n) for n in range(87)]) # Michael S. Branicky, Jul 05 2022

Formula

Fixed point of the morphism 0 -> 0,1; 1 -> 2,3; 2 -> 1,0; 3 -> 3,2 starting from 0.