A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 11, 18, 27, 16, 25, 14, 21, 20, 13, 30, 45, 24, 17, 22, 33, 36, 23, 54, 81, 32, 19, 50, 75, 28, 35, 42, 63, 40, 55, 26, 39, 60, 37, 90, 135, 48, 49, 34, 51, 44, 29, 66, 99, 72, 41, 46, 69, 108, 91, 162, 243, 64, 85, 38, 57, 100, 125, 150, 225, 56, 31, 70, 105, 84, 47, 126, 189, 80, 43, 110, 165, 52

Offset

1,2

Comments

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains 2n, while the value of right hand child is obtained by applying A250469(1+n):

1

|

................../ \..................

2 3

4......../ \........5 6......../ \........9

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

8 7 10 15 12 11 18 27

16 25 14 21 20 13 30 45 24 17 22 33 36 23 54 81

etc.

Note how all nodes with odd n have a right hand child with value 3n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..6142

Antti Karttunen, Entanglement Permutations, 2016-2017

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A269865 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269865 (/ n 2)))) (else (A250469 (+ 1 (A269865 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A269866.

Cf. A250469.

Related or similar permutations: A269359, A269863, A269864, A269867, A246375, A249814, A252755, A270195.

Sequence in context: A246376 A269866 A246375 * A269387 A207801 A340364

Adjacent sequences: A269862 A269863 A269864 * A269866 A269867 A269868

Keyword

nonn,tabf,look

Author

Antti Karttunen, Mar 12 2016

Status

approved