A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

1, 4, 2, 12, 6, 7, 3, 30, 19, 18, 10, 21, 11, 9, 5, 74, 48, 52, 32, 49, 31, 25, 15, 54, 36, 27, 16, 24, 14, 17, 8, 172, 125, 118, 85, 128, 89, 76, 51, 119, 86, 75, 50, 64, 43, 38, 26, 132, 92, 83, 61, 68, 45, 41, 28, 60, 40, 35, 22, 42, 29, 23, 13, 383, 314, 275, 219, 266, 208, 201, 152, 283, 227, 207, 159, 174, 129, 127, 88

Offset

1,2

Comments

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

|

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

4 2

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

30 19 18 10 21 11 9 5

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

etc.

Note how this is a mirror image of the tree shown in A260432.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences that are permutations of the natural numbers

Formula

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

As a composition of other permutations:

a(n) = A260432(A054429(n)).

a(n) = A260430(A260432(n)).

Prog

(Scheme, with memoizing macro definec)
(definec (A260434 n) (cond ((<= n 1) n) ((even? n) (A257803 (+ 1 (A260434 (/ n 2))))) (else (A257804 (A260434 (/ (- n 1) 2))))))

Crossrefs

Inverse: A260433.

Related permutations: A260432, A260430, A054429.

Cf. A257803, A257804, A257807, A257808.

Cf. also A233271, A257806.

Sequence in context: A077015 A077016 A191436 * A243344 A293603 A201825

Adjacent sequences: A260431 A260432 A260433 * A260435 A260436 A260437

Keyword

nonn,tabf,look

Author

Antti Karttunen, Jul 27 2015

Status

approved