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

0,3

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.

Links

Kevin Ryde, Table of n, a(n) for n = 0..8192

Index entries for sequences that are fixed points of mappings

Formula

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

Example

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

Mathematica

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

Prog

(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

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).

Sequence in context: A293113 A366528 A154720 * A071501 A004572 A352799

Adjacent sequences: A355484 A355485 A355486 * A355488 A355489 A355490

Keyword

nonn,base,easy

Author

Kevin Ryde, Jul 04 2022

Status

approved