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A246208 Permutation of nonnegative integers: a(0) = 0, a(1) = 1, and for n > 1, if A117966(n) < 1, a(n) = 2*a(-(A117966(n))), otherwise a(n) = 1 + 2*a(A117966(n)-1). 6
0, 1, 2, 5, 11, 3, 10, 4, 22, 45, 91, 9, 19, 39, 183, 7, 21, 23, 90, 44, 182, 20, 6, 8, 38, 18, 78, 157, 315, 37, 75, 151, 631, 17, 77, 13, 27, 55, 155, 311, 623, 111, 1263, 35, 303, 47, 181, 43, 365, 41, 89, 367, 15, 79, 314, 156, 630, 76, 16, 36, 150, 74, 302, 180, 46, 88, 14, 366, 42, 40, 364, 12, 54, 26, 110, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

Thus this shares with A140264 the property that apart from a(0) = 0, even numbers occur only in positions given by A117968, and odd numbers only in positions given by A117967.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..6561

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(0) = 0, a(1) = 1, and for n > 1, if A117966(n) < 1, a(n) = 2*a(-(A117966(n))), otherwise a(n) = 1 + 2*a(A117966(n)-1).

As a composition of related permutations:

a(n) = A054429(A246210(n)).

a(n) = A246210(A246211(n)).

PROG

(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)

(definec (A246208 n) (cond ((<= n 1) n) ((negative? (A117966 n)) (* 2 (A246208 (- (A117966 n))))) (else (+ 1 (* 2 (A246208 (- (A117966 n) 1)))))))

(Python)

def a117966(n):

    if n==0: return 0

    if n%3==0: return 3*a117966(n/3)

    elif n%3==1: return 3*a117966((n - 1)/3) + 1

    else: return 3*a117966((n - 2)/3) - 1

def a(n):

    if n<2: return n

    x=a117966(n)

    if x<1: return 2*a(-x)

    else: return 1 + 2*a(x - 1)

print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 07 2017

CROSSREFS

Inverse: A246207.

Related permutations: A140264, A054429, A246210, A246211.

Cf. A005408, A005843, A117966, A117967, A117968.

Sequence in context: A018862 A175310 A175311 * A286091 A127011 A170868

Adjacent sequences:  A246205 A246206 A246207 * A246209 A246210 A246211

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 19 2014

STATUS

approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)