A234025 Permutation of nonnegative integers: a(n) = A054429(A193231(n)).

0, 1, 2, 3, 6, 7, 5, 4, 8, 9, 11, 10, 13, 12, 14, 15, 30, 31, 29, 28, 27, 26, 24, 25, 17, 16, 18, 19, 20, 21, 23, 22, 44, 45, 47, 46, 41, 40, 42, 43, 35, 34, 32, 33, 38, 39, 37, 36, 61, 60, 62, 63, 56, 57, 59, 58, 50, 51, 49, 48, 55, 54, 52, 53, 106, 107, 105

Offset: 0

Author

Antti Karttunen, Dec 28 2013

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A234026.

Programs

Python

def a065621(n): return n^(2*(n - (n&-n)))
def a048724(n): return n^(2*n)
def a054429(n): return 1 if n==1 else 2*a054429(int(n/2)) + 1 - n%2
def a193231(n):
    if n<2: return n
    if n%2==0: return a048724(a193231(n/2))
    else: return a065621(1 + a193231((n - 1)/2))
def a(n): return n if n<2 else a054429(a193231(n)) # Indranil Ghosh, Jun 05 2017

Scheme

(define (A234025 n) (A054429 (A193231 n)))

Formula

a(n) = A054429(A193231(n)).

a(n) = A234027(A054429(n)).