A257726 a(0)=0; a(2n) = unlucky(a(n)), a(2n+1) = lucky(a(n)+1), where lucky = A000959, unlucky = A050505.

0, 1, 2, 3, 4, 7, 5, 9, 6, 13, 11, 25, 8, 15, 14, 33, 10, 21, 19, 51, 17, 43, 35, 115, 12, 31, 22, 67, 20, 63, 45, 163, 16, 37, 29, 93, 27, 79, 66, 273, 24, 73, 57, 223, 47, 171, 146, 723, 18, 49, 42, 151, 30, 99, 88, 385, 28, 87, 83, 349, 59, 235, 203, 1093, 23, 69, 50, 193, 40, 135, 119, 559, 38, 129, 102, 475, 86, 367, 335, 1983, 34, 111

Offset

0,3

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A050505(n), and each right hand child as A000959(1+n), when a parent contains n >= 1:

0

|

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

2 3

4......../ \........7 5......../ \........9

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

6 13 11 25 8 15 14 33

10 21 19 51 17 43 35 115 12 31 22 67 20 63 45 163

etc.

Because all lucky numbers are odd, it means that even terms can only occur in even positions (together with odd unlucky numbers, for each one of which there is a separate infinite cycle), while terms in odd positions are all odd.

Links

Antti Karttunen, Table of n, a(n) for n = 0..512

Index entries for sequences that are permutations of the natural numbers

Formula

a(0)=0; after which, a(2n) = A050505(a(n)), a(2n+1) = A000959(a(n)+1).

As a composition of other permutations. For all n >= 1:

a(n) = A257731(A246378(n)).

a(n) = A257733(A237126(n)).

a(n) = A257801(A257728(n)).

Prog

(Scheme, with memoizing definec-macro)
(definec (A257726 n) (cond ((zero? n) n) ((even? n) (A050505 (A257726 (/ n 2)))) (else (A000959 (+ 1 (A257726 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A257725.

Cf. A000959, A050505, A005408, A005843.

Related or similar permutations: A237126, A246378, A257728, A257731, A257733, A257801.

Cf. also A183089 (another similar permutation, but with a slightly different definition, resulting the first differing term at n=9, where a(9) = 13, while A183089(9) = 21).

Cf. also A257735 - A257738.

Sequence in context: A125150 A265901 A257801 * A183089 A191544 A191438

Adjacent sequences: A257723 A257724 A257725 * A257727 A257728 A257729

Keyword

nonn,tabf

Author

Antti Karttunen, May 06 2015

Status

approved