A269387 Tree of Ludic sieve: a(0) = 1, a(1) = 2; after which, a(2n) = A269379(a(n)), a(2n+1) = 2*a(n).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 19, 18, 21, 16, 11, 14, 27, 20, 35, 30, 33, 24, 31, 38, 51, 36, 49, 42, 45, 32, 13, 22, 39, 28, 65, 54, 57, 40, 59, 70, 87, 60, 79, 66, 69, 48, 55, 62, 111, 76, 125, 102, 105, 72, 85, 98, 123, 84, 109, 90, 93, 64, 17, 26, 63, 44, 95, 78, 81, 56, 113, 130, 159, 108, 139, 114, 117, 80

Offset

0,2

Comments

Permutation of natural numbers obtained from the Ludic sieve. Note the indexing: Domain starts from 0, range from 1.

This sequence can be represented as a binary tree. Each left hand child is obtained by applying A269379 to the parent's contents, and each right hand child is obtained by doubling the parent's contents:

1

|

...................2...................

3 4

5......../ \........6 9......../ \........8

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

7 10 15 12 19 18 21 16

11 14 27 20 35 30 33 24 31 38 51 36 49 42 45 32

etc.

Sequence A269385 is obtained from the mirror image of the same tree.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences that are permutations of the natural numbers

Formula

a(0) = 1, a(1) = 2; after which, a(2n) = A269379(a(n)), a(2n+1) = 2*a(n).

As a composition of other permutations:

a(n) = A269171(A252753(n)).

a(n) = A260741(A269377(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A269387 n) (cond ((<= n 2) (+ 1 n)) ((even? n) (A269379 (A269387 (/ n 2)))) (else (* 2 (A269387 (/ (- n 1) 2))))))

Crossrefs

Inverse: A269388.

Cf. A003309 (left edge of the tree).

Cf. A269379.

Related permutations: A260741, A269171, A269385.

Cf. also A252753, A269377.

Sequence in context: A269866 A246375 A269865 * A207801 A340364 A324106

Adjacent sequences: A269384 A269385 A269386 * A269388 A269389 A269390

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 01 2016

Status

approved