A254104 Permutation of natural numbers: a(0) = 0, a(3n) = 1 + 2*a(2n - 1), a(3n+1) = 1 + 2*a(2n), a(3n+2) = 2*a(n+1).

0, 1, 2, 3, 5, 4, 7, 11, 6, 9, 15, 10, 23, 13, 8, 19, 31, 14, 21, 47, 22, 27, 17, 12, 39, 63, 18, 29, 43, 30, 95, 45, 20, 55, 35, 46, 25, 79, 26, 127, 37, 16, 59, 87, 38, 61, 191, 62, 91, 41, 28, 111, 71, 42, 93, 51, 94, 159, 53, 44, 255, 75, 54, 33, 119, 34, 175, 77, 24, 123, 383, 78, 125, 183, 126, 83, 57, 36, 223, 143, 58, 85, 187, 86, 103, 189, 60

Offset: 0

Author

Antti Karttunen, Jan 25 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..9842
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A254103.

Cf. A007051, A016789, A032766, A064216, A253887.

Programs

Python

def a(n):
    if n==0: return 0
    if n%3==0: return 1 + 2*a(2*n//3 - 1)
    elif n%3==1: return 1 + 2*a(2*(n - 1)//3)
    else: return 2*a((n - 2)//3 + 1)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 06 2017

Formula

a(0) = 0, a(3n) = 1 + 2*a(2n - 1), a(3n+1) = 1 + 2*a(2n), a(3n+2) = 2*a(n+1).

Other identities:

a(A007051(n)) = 2^n for all n >= 0. [A property shared with A064216.]