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

0,3

Links

A. Karttunen, Table of n, a(n) for n = 0..1023

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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.

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 *)

Prog

(Scheme) (define (A163241 n) (+ (A000695 (A003987bi (A059905 n) (A059906 n))) (* 2 (A000695 (A059906 n)))))
(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)<<i for i in range(len(bin(n)[2:])//2 + 1)])
def a059906(n):
    x=[int(k) for k in list(bin(n)[2:])][::-1]
    return sum([x[2*i + 1]*2**i for i in range(len(x)//2)])
def a(n): return a000695(a059905(n)^a059906(n)) + 2*a000695(a059906(n))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 26 2017
(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
(C) uint32_t a(uint32_t n) { return n ^ ((n >> 1) & 0x55555555); } // Falk Hüffner, Jan 22 2022

Crossrefs

Cf. A048647, A007090, A003987.

Sequence in context: A116966 A182187 A334652 * A234027 A364839 A165279

Adjacent sequences: A163238 A163239 A163240 * A163242 A163243 A163244

Keyword

nonn,base,easy

Author

Antti Karttunen, Jul 29 2009

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009

Status

approved