A284572 Permutation of natural numbers: a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A065642(1+a(n)).

1, 2, 4, 3, 9, 6, 25, 5, 8, 14, 20, 10, 49, 39, 52, 7, 12, 13, 27, 22, 45, 33, 63, 15, 121, 79, 80, 65, 50, 85, 2809, 11, 16, 19, 169, 21, 28, 42, 56, 35, 529, 73, 92, 55, 68, 103, 128, 23, 32, 199, 244, 130, 100, 131, 243, 106, 132, 82, 153, 139, 172, 4619, 5620, 17, 18, 26, 289, 31, 40, 277, 340, 34, 44, 43, 841, 69, 1849, 91, 171, 58, 48

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A005117(1+n), and each right hand child as A065642(1+n), when the parent node contains n:

1

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

2 4

3......../ \........9 6......../ \........25

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

5 8 14 20 10 49 39 52

7 12 13 27 22 45 33 63 15 121 79 80 65 50 85 2809

etc.

Compare to A285112.

Links

Antti Karttunen, Table of n, a(n) for n = 1..166

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A065642(1+a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A284572 n) (cond ((= 1 n) n) ((even? n) (A005117 (+ 1 (A284572 (/ n 2))))) (else (A065642 (+ 1 (A284572 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A284571.

Cf. A005117, A065642.

Similar or related permutations: A243344, A243346, A277696, A285112.

Sequence in context: A129596 A356222 A329901 * A157182 A343232 A292145

Adjacent sequences: A284569 A284570 A284571 * A284573 A284574 A284575

Keyword

nonn,tabf

Author

Antti Karttunen, Apr 17 2017

Status

approved