A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

0, 1, 2, 3, 6, 4, 8, 5, 24, 10, 12, 7, 30, 13, 14, 9, 120, 34, 36, 16, 48, 18, 26, 11, 144, 42, 50, 19, 54, 20, 32, 15, 720, 154, 156, 46, 168, 49, 60, 22, 240, 66, 72, 25, 126, 37, 38, 17, 840, 186, 192, 58, 246, 68, 74, 27, 264, 73, 78, 28, 150, 44, 56, 21, 5040, 874, 876, 199, 888, 202, 204, 64, 960, 216, 242, 67, 288, 82, 84, 31

Offset

0,3

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A153880(n), and each right hand child as A273670(n), when their parent contains n >= 1:

0

|

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

2 3

6......../ \........4 8......../ \........5

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

24 10 12 7 30 13 14 9

120 34 36 16 48 18 26 11 144 42 50 19 54 20 32 15

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 0..1023

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

Formula

a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A273666 n) (cond ((zero? n) n) ((even? n) (A153880 (A273666 (/ n 2)))) (else (A273670 (A273666 (/ (- n 1) 2))))))

Crossrefs

Inverse: A273665.

Cf. A153880, A273670.

Related or similar permutations: A255566, A273668.

Sequence in context: A036552 A257987 A132169 * A302023 A112975 A257218

Adjacent sequences: A273663 A273664 A273665 * A273667 A273668 A273669

Keyword

nonn,base,tabf

Author

Antti Karttunen, May 30 2016

Status

approved