A163241 Simple self-inverse permutation: Write n in base 4, then replace each digit '2' with '3' and vice versa, then convert back to decimal.

0, 1, 3, 2, 4, 5, 7, 6, 12, 13, 15, 14, 8, 9, 11, 10, 16, 17, 19, 18, 20, 21, 23, 22, 28, 29, 31, 30, 24, 25, 27, 26, 48, 49, 51, 50, 52, 53, 55, 54, 60, 61, 63, 62, 56, 57, 59, 58, 32, 33, 35, 34, 36, 37, 39, 38, 44, 45, 47, 46, 40, 41, 43, 42, 64, 65, 67, 66, 68, 69, 71, 70

Offset: 0

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• base
• easy

Examples

			43 in quaternary base (A007090) is written as '223' (2*16 + 2*4 + 3), which is then mapped to '332' = 3*16 + 3*4 + 2 = 62, thus a(43) = 62, and likewise a(62) = 43.
		

Links

• A. Karttunen, Table of n, a(n) for n = 0..1023
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A048647, A007090, A003987.

Programs

C

uint32_t a(uint32_t n) { return n ^ ((n >> 1) & 0x55555555); } // Falk Hüffner, Jan 22 2022

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      a(iquo(n, 4, 'r'))*4+[0, 1, 3, 2][r+1])
    end:
seq(a(n), n=0..71);  # Alois P. Heinz, Jan 25 2022

Mathematica

Table[FromDigits[IntegerDigits[n,4]/.{2->a,3->b}/.{a->3,b->2},4],{n,0,75}] (* Harvey P. Dale, Nov 29 2011 *)

PARI

f(d) = if (d==2, 4, if (x==d, 2, d));
a(n) = fromdigits(apply(f, digits(n, 4)), 4); \\ Michel Marcus, Jun 28 2017

Python

def a000695(n):
    n=bin(n)[2:]
    x=len(n)
    return sum([int(n[i])*4**(x - 1 - i) for i in range(x)])
def a059905(n): return sum([(n>>2*i&1)<Indranil Ghosh, Jun 26 2017

Scheme

(define (A163241 n) (+ (A000695 (A003987bi (A059905 n) (A059906 n))) (* 2 (A000695 (A059906 n)))))

Formula

a(n) = A000695(A003987bi(A059905(n),A059906(n))) + 2*A000695(A059906(n)), where A003987bi is binary XOR.

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009