A275716 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).

1, 2, 9, 3, 42, 17, 12, 4, 209, 115, 82, 41, 59, 26, 19, 5, 1042, 801, 572, 444, 409, 283, 202, 57, 292, 180, 129, 48, 92, 31, 22, 6, 5209, 5603, 4002, 4881, 2859, 3106, 2219, 733, 2042, 1977, 1412, 620, 1009, 395, 282, 97, 1459, 1258, 899, 525, 642, 334, 239, 74, 459, 213, 152, 63, 109, 40, 29, 7, 26042, 39217

Offset

0,2

Comments

Note the indexing: the domain starts from 0, while the range excludes zero.

This sequence can be represented as a binary tree. Each left hand child is obtained by applying A273669(n) when the parent contains n, and each right hand child is obtained by applying A273664 to the parent's contents:

1

|

...................2...................

9 3

42......../ \........17 12......../ \........4

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

209 115 82 41 59 26 19 5

1042 801 572 444 409 283 202 57 292 180 129 48 92 31 22 6

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 0..4095

Index entries for sequences that are permutations of the natural numbers

Formula

a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).

As a composition of other permutations:

a(n) = A249824(A163511(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A275716 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A273669 (A275716 (/ n 2)))) (else (A273664 (A275716 (/ (- n 1) 2))))))

Crossrefs

Inverse: A275715.

Cf. A273664, A273669.

Related or similar permutations: A163511, A249824, A245612.

Sequence in context: A237860 A088614 A162615 * A295197 A155163 A309929

Adjacent sequences: A275713 A275714 A275715 * A275717 A275718 A275719

Keyword

nonn,tabf

Author

Antti Karttunen, Aug 06 2016

Status

approved