A353167 -id:A353167 - cp's OEIS frontend

A048725 a(n) = Xmult(n,5) or rule90(n,1).

0, 5, 10, 15, 20, 17, 30, 27, 40, 45, 34, 39, 60, 57, 54, 51, 80, 85, 90, 95, 68, 65, 78, 75, 120, 125, 114, 119, 108, 105, 102, 99, 160, 165, 170, 175, 180, 177, 190, 187, 136, 141, 130, 135, 156, 153, 150, 147, 240, 245, 250, 255, 228, 225, 238, 235, 216, 221, 210

Offset: 0

Antti Karttunen, Apr 26 1999

The orbit of 1 under iteration of this function is the Sierpinski gasket A038183. It is called "rule 90" because the 8 bits of 90 = 01011010 in binary give bit k of the result as function of the value in {0,...,7} made out of bits k,k+1,k+2 of the input (i.e., floor(input / 2^k) mod 8). - M. F. Hasler, Oct 09 2017

			   n (in binary) | 4n [binary] | n XOR 4n [binary] | [decimal] = a(n)
          0      |        0    |           0       |        0
          1      |      100    |         101       |        5
         10      |     1000    |        1010       |       10
         11      |     1100    |        1111       |       15
        100      |    10000    |       10100       |       20
        101      |    10100    |       10001       |       17
   etc.

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Cf. A048720, A048705, A048710, A048724, A048727, A048729.
Cf. A038183.
Cf. A353167 (terms sorted).

a:= n-> Bits[Xor](n*4, n):
seq(a(n), n=0..120);  # Alois P. Heinz, Aug 24 2019

Table[ BitXor[4n, n], {n, 0, 60}] (* Robert G. Wilson v, Jul 06 2006 *)

a(n)=bitxor(n,4*n) \\ Charles R Greathouse IV, Oct 03 2016

def A048725(n): return n^ n<<2 # Chai Wah Wu, Jun 29 2022

a(n) = n XOR n*2 XOR (n XOR n*2)*2 = A048724(A048724(n)). - Reinhard Zumkeller, Nov 12 2004

a(n) = n XOR (4n). - M. F. Hasler, Oct 09 2017

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

Original entry on oeis.org

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

Kevin Ryde, Jul 04 2022

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.

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

Cf. A030373 (base 4 digits), A003987 (XOR).
Cf. A341389, A269723, A010060.
Cf. A353167 (indices of 0's).
Other digit operations: A053737 (sum), A309954 (product).

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

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

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

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

cp's OEIS Frontend

A048725 a(n) = Xmult(n,5) or rule90(n,1).

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