A115304 a(n) = n if n < 4, otherwise 4*a(floor(n/4)) + 3 - n mod 4.

1, 2, 3, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 127, 126, 125, 124, 123, 122, 121

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2006

Keywords

• nonn
• base

Comments

Self-inverse permutation of the natural numbers.

If n is written in base-4 representation, then a(n) is the value after replacing all digits d (except for the leading one) by 3-d.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A054429, A102572, A115303, A115305, A115306, A115307, A115308, A115309, A106649.

Programs

Mathematica

A115304[n_] := FromDigits[MapAt[3 - # &, IntegerDigits[n, 4], 2;;], 4];
Array[A115304, 100] (* Paolo Xausa, May 20 2024 *)

Python

def A115304(n): # according to Formula by Alan Michael Gómez Calderón
    m = 4**floor(log(n,4))-1
    return n^m # A.H.M. Smeets, Apr 01 2025

Formula

a(n) = A115310(n+2,3).

a(n) = n XOR (4^A102572(n) - 1). - Alan Michael Gómez Calderón, Mar 27 2025

a(a(n)) = n. - A.H.M. Smeets, Apr 01 2025