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A355487
Bitwise XOR of the base-4 digits of n.
2
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.
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. A353167 (indices of 0's).
Other digit operations: A053737 (sum), A309954 (product).
Sequence in context: A293113 A366528 A154720 * A071501 A004572 A352799
KEYWORD
nonn,base,easy
AUTHOR
Kevin Ryde, Jul 04 2022
STATUS
approved