A270202 Permutation of natural numbers: a(1) = 1, a(2n) = A270189(1+a(n)), a(2n+1) = A270190(a(n)).

1, 2, 9, 3, 11, 12, 36, 4, 15, 14, 39, 17, 40, 52, 108, 5, 16, 22, 51, 20, 47, 59, 114, 25, 55, 60, 118, 77, 167, 156, 312, 6, 18, 24, 54, 30, 73, 75, 165, 28, 67, 68, 139, 85, 185, 166, 339, 34, 84, 80, 174, 87, 187, 173, 347, 117, 227, 254, 496, 236, 461, 475, 852, 7, 21, 26, 56, 33, 76, 79, 170, 43, 99, 112, 216, 115, 219, 251, 490, 41

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A270189(1+n), and each right hand child as A270190(n), when the parent node contains n:

1

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

2 9

3......../ \........11 12......../ \........36

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

4 15 14 39 17 40 52 108

5 16 22 51 20 47 59 114 25 55 60 118 77 167 156 312

etc.

Links

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

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A270189(1+a(n)), a(2n+1) = A270190(a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A270202 n) (cond ((= 1 n) n) ((even? n) (A270189 (+ 1 (A270202 (/ n 2))))) (else (A270190 (A270202 (/ (- n 1) 2))))))

Crossrefs

Inverse: A270201.

Cf. A270189, A270190.

Similar permutation: A270194.

Sequence in context: A366249 A302973 A258403 * A379402 A379293 A171534

Adjacent sequences: A270199 A270200 A270201 * A270203 A270204 A270205

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 16 2016

Status

approved