A260432 Permutation of natural numbers: a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

1, 2, 4, 3, 7, 6, 12, 5, 9, 11, 21, 10, 18, 19, 30, 8, 17, 14, 24, 16, 27, 36, 54, 15, 25, 31, 49, 32, 52, 48, 74, 13, 23, 29, 42, 22, 35, 40, 60, 28, 41, 45, 68, 61, 83, 92, 132, 26, 38, 43, 64, 50, 75, 86, 119, 51, 76, 89, 128, 85, 118, 125, 172, 20, 34, 39, 57, 47, 73, 71, 106, 37, 55, 59, 82, 67, 96, 101, 140, 46, 70, 69

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A257804(n), and each right hand child as A257803(1+n), when the parent contains n:

|

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

2 4

3......../ \........7 6......../ \........12

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

5 9 11 21 10 18 19 30

8 17 14 24 16 27 36 54 15 25 31 49 32 52 48 74

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)).

As a composition of other permutations:

a(n) = A260434(A054429(n)).

a(n) = A260430(A260434(n)).

Prog

(Scheme, with memoizing macro definec)
(definec (A260432 n) (cond ((<= n 1) n) ((even? n) (A257804 (A260432 (/ n 2)))) (else (A257803 (+ 1 (A260432 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A260431.

Related permutations: A260434, A260430, A054429.

Cf. A257803, A257804, A257807, A257808.

Cf. also A233271, A257806.

Sequence in context: A266413 A245614 A246165 * A021808 A365215 A225252

Adjacent sequences: A260429 A260430 A260431 * A260433 A260434 A260435

Keyword

nonn,tabf

Author

Antti Karttunen, Jul 27 2015

Status

approved