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

Author

Antti Karttunen, Apr 26 1999

Keywords

• nonn
• easy

Comments

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

Examples

			   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.
		

Links

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

Crossrefs

Cf. A048720, A048705, A048710, A048724, A048727, A048729.

Cf. A038183.

Cf. A353167 (terms sorted).

Programs

Maple

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

Mathematica

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

PARI

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

Python

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

Formula

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