A269366 a(1) = 1, a(2n) = A269361(1+a(n)), a(2n+1) = A269363(a(n)).

1, 2, 3, 4, 6, 5, 7, 8, 12, 16, 15, 9, 11, 10, 22, 13, 24, 18, 38, 40, 48, 33, 46, 20, 14, 32, 27, 17, 19, 25, 44, 29, 28, 50, 75, 21, 30, 72, 71, 73, 70, 133, 139, 113, 76, 129, 91, 42, 35, 36, 23, 37, 54, 45, 51, 26, 43, 49, 39, 82, 62, 128, 107, 80, 56, 53, 83, 114, 140, 109, 214, 52, 59, 34, 47, 149, 150, 141, 123, 221, 111, 121

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A269361(1+n), and each right hand child as A269363(n), when the parent node contains n:

|

...................1...................

2 3

4......../ \........6 5......../ \........7

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

8 12 16 15 9 11 10 22

13 24 18 38 40 48 33 46 20 14 32 27 17 19 25 44

etc.

An example of (suspected) "entanglement permutation" where the other pair of complementary sequences is generated by a greedy algorithm.

Sequence is not only injective, but also surjective on N (thus a permutation of natural numbers) provided that A269361 is surjective on A091072 and A269363 is surjective on A091067.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Antti Karttunen, Entanglement Permutations, 2016-2017

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(defineperm1 (A269366 n) (cond ((= 1 n) n) ((even? n) (A269361 (+ 1 (A269366 (/ n 2))))) (else (A269363 (A269366 (/ (- n 1) 2))))))
(define (A269365 n) (A269366 (- n))) ;; The negative side gives the values for the inverse function (from the cache).
;; We consider a > b (i.e. not less than b) also in case a is #f.
;; (Because of the stateful caching system used by defineperm1-macro):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

Crossrefs

Left inverse: A269365 (also right inverse, if this sequence is a permutation of natural numbers).

Cf. A091067, A091072, A269361, A269363, A269367, A266121.

Sequence in context: A059893 A331274 A269365 * A361481 A275376 A342798

Adjacent sequences: A269363 A269364 A269365 * A269367 A269368 A269369

Keyword

nonn,look,tabf

Author

Antti Karttunen, Feb 25 2016

Status

approved