A262692 Permutation of natural numbers: a(1) = 1; thereafter a(2n) = A182859(1+a(n)), a(2n+1) = A080218(a(n)).

1, 2, 3, 4, 5, 9, 6, 12, 7, 16, 8, 25, 14, 18, 10, 32, 19, 20, 11, 45, 26, 24, 13, 66, 38, 42, 22, 49, 29, 28, 15, 81, 53, 50, 31, 52, 33, 30, 17, 121, 73, 68, 39, 64, 37, 40, 21, 175, 106, 104, 61, 114, 69, 56, 35, 135, 82, 76, 46, 75, 43, 44, 23, 231, 129, 147, 86, 136, 83, 80, 51, 144, 85, 88, 55, 78, 47, 48, 27, 338, 197, 190, 118, 182, 108, 105, 62, 172, 101, 102, 60, 110, 65, 54, 34

Offset

1,2

Comments

This sequence can be represented as a binary tree. For each node containing n, the left hand child is obtained as A182859(1+n), and the right hand child as A080218(n):

1

|

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

2 3

4......../ \........5 9......../ \........6

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

12 7 16 8 25 14 18 10

32 19 20 11 45 26 24 13 66 38 42 22 49 29 28 15

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..4095

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1; thereafter a(2n) = A182859(1+a(n)), a(2n+1) = A080218(a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A262692 n) (cond ((<= n 1) n) ((even? n) (A182859 (+ 1 (A262692 (/ n 2))))) (else (A080218 (A262692 (/ (- n 1) 2))))))

Crossrefs

Inverse: A262691.

Cf. A080218, A182859.

Sequence in context: A124652 A250552 A048623 * A346097 A346098 A245821

Adjacent sequences: A262689 A262690 A262691 * A262693 A262694 A262695

Keyword

nonn,tabf

Author

Antti Karttunen, Sep 28 2015

Status

approved