A246209 - OEIS

%I #24 May 02 2021 11:09:09

%S 0,1,5,2,15,22,3,7,52,66,35,71,4,6,11,23,137,194,148,213,36,73,99,172,

%T 17,8,16,21,12,25,33,58,462,601,447,643,431,620,304,516,37,72,104,173,

%U 127,225,419,587,45,64,9,19,47,68,49,69,13,24,29,59,43,75,152,197,1273,1734,1334,1940,1294,1740,899,1556,1404,1837,945,1567,389,698,1246,1761,41

%N Permutation of nonnegative integers: a(0) = 0, a(1) = 1, a(2n) = A117967(1+a(n)), a(2n+1) = A117968(a(n)).

%C This is an instance of entanglement permutation, where complementary pair A005843/A005408 (even and odd numbers respectively) is entangled with complementary pair A117967/A117968 (positive and negative part of inverse of balanced ternary enumeration of integers, respectively), with a(0) set to 0 and a(1) set to 1.

%C This implies that the even positions contain only terms of A117967 and apart from a(1) = 1, the odd positions contain only terms of A117968.

%H Antti Karttunen, <a href="/A246209/b246209.txt">Table of n, a(n) for n = 0..2047</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(0) = 0, a(1) = 1, a(2n) = A117967(1+a(n)), a(2n+1) = A117968(a(n)).

%F As a composition of related permutations:

%F a(n) = A246207(A054429(n)).

%F a(n) = A246211(A246207(n)).

%o (Scheme, with memoizing definec-macro from _Antti Karttunen_'s IntSeq-library)

%o (definec (A246209 n) (cond ((<= n 1) n) ((odd? n) (A117968 (A246209 (/ (- n 1) 2)))) ((even? n) (A117967 (+ 1 (A246209 (/ n 2)))))))

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def a004488(n): return int("".join(str((3 - i)%3) for i in digits(n, 3)[1:]), 3)

%o def a117968(n):

%o     if n==1: return 2

%o     if n%3==0: return 3*a117968(n//3)

%o     elif n%3==1: return 3*a117968((n - 1)//3) + 2

%o     else: return 3*a117968((n + 1)//3) + 1

%o def a117967(n): return 0 if n==0 else a117968(-n) if n<0 else a004488(a117968(n))

%o def a(n): return n if n<2 else a117967(1 + a(n//2)) if n%2==0 else a117968(a((n - 1)//2))

%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 07 2017

%Y Inverse: A246210.

%Y Related permutations: A054429, A246207, A246211.

%Y Cf. A117967, A117968.

%K nonn

%O 0,3

%A _Antti Karttunen_, Aug 19 2014