%I #29 Mar 26 2021 09:25:35
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,19,14,15,16,17,18,13,20,21,22,27,24,35,
%T 38,23,28,39,30,31,32,33,34,25,36,41,26,29,40,37,42,43,44,75,54,59,48,
%U 67,70,51,76,83,46,55,56,71,78,47,60,79,62,63,64,65,66,49,68,81,50,57,72,73,82,45,52,77,58,61,80,69
%N Self-inverse permutation of natural numbers: a(n) = A057889(3*n) / 3.
%C In binary system, 3 ("11" in binary), has a similar shortcut rule for divisibility as eleven has in decimal system. This rule doesn't depend on which end of the number representation it is applied from, thus, if we reverse the number 3*n with "balanced bit-reverse" (A057889), the result should still be divisible by 3. Moreover, because the reversing operation is itself a self-inverse involution, and the prime factorization of any natural number is unique, we get a self-inverse permutation of nonnegative integers when we divide the bit-reversed result with 3.
%H Antti Karttunen, <a href="/A246200/b246200.txt">Table of n, a(n) for n = 0..10921</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A057889(3*n) / 3.
%o (Scheme) (define (A246200 n) (/ (A057889 (* 3 n)) 3))
%o (Python)
%o def a057889(n):
%o x=bin(n)[2:]
%o y=x[::-1]
%o return int(str(int(y))+(len(x) - len(str(int(y))))*'0', 2)
%o def a(n): return a057889(3*n)//3
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 11 2017
%Y Cf. A036215, A057889, A003714, A048724, A083822, A083824.
%K nonn,base,look
%O 0,3
%A _Antti Karttunen_, Aug 27 2014