A246210 - OEIS

A246210

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

0, 1, 3, 6, 12, 2, 13, 7, 25, 50, 100, 14, 28, 56, 200, 4, 26, 24, 101, 51, 201, 27, 5, 15, 57, 29, 113, 226, 452, 58, 116, 232, 904, 30, 114, 10, 20, 40, 228, 456, 912, 80, 1808, 60, 464, 48, 202, 52, 402, 54, 102, 400, 8, 112, 453, 227, 905, 115, 31, 59, 233, 117, 465, 203, 49, 103, 9, 401, 53, 55, 403, 11, 41, 21, 81, 61

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OFFSET

0,3

COMMENTS

This is an instance of entanglement permutation, where complementary pair A117967/A117968 (positive and negative 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.

This implies that apart from a(1) = 1, even numbers occur only in positions given by A117967, and odd numbers only in positions given by A117968.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..2187

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) = 1 + 2*a(-(A117966(n))), otherwise a(n) = 2*a(A117966(n)-1).

As a composition of related permutations:

a(n) = A054429(A246208(n)).

a(n) = A246208(A246211(n)).

PROG

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

(definec (A246210 n) (cond ((<= n 1) n) ((negative? (A117966 n)) (+ 1 (* 2 (A246210 (- (A117966 n)))))) (else (* 2 (A246210 (- (A117966 n) 1))))))