A269385 Tree of Ludic sieve, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)).

1, 2, 4, 3, 8, 9, 6, 5, 16, 21, 18, 19, 12, 15, 10, 7, 32, 45, 42, 49, 36, 51, 38, 31, 24, 33, 30, 35, 20, 27, 14, 11, 64, 93, 90, 109, 84, 123, 98, 85, 72, 105, 102, 125, 76, 111, 62, 55, 48, 69, 66, 79, 60, 87, 70, 59, 40, 57, 54, 65, 28, 39, 22, 13, 128, 189, 186, 229, 180, 267, 218, 191, 168, 249, 246, 305, 196, 291, 170, 151, 144

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 doubling the parent's contents, and each right hand child is obtained by applying A269379 to the parent's contents:

1

|

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

4 3

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

16 21 18 19 12 15 10 7

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

etc.

Sequence A269387 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) = 2*a(n), a(2n+1) = A269379(a(n)).

As a composition of related permutations:

a(n) = A269171(A252755(n)).

a(n) = A260741(A269375(n)).

Other identities. For all n >= 2:

A000035(a(n)) = A000035(n). [This permutation preserves the parity of n from a(2)=4 onward.]

Prog

(Scheme, with memoization-macro definec)
(definec (A269385 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269385 (/ n 2)))) (else (A269379 (A269385 (/ (- n 1) 2))))))

Crossrefs

Inverse: A269386.

Cf. A000035, A269379.

Cf. A003309 (right edge of the tree).

Related or similar permutations: A163511, A260741, A269387, A269171.

Cf. also A252755, A269375.

Sequence in context: A284457 A365656 A182944 * A252755 A366275 A163511

Adjacent sequences: A269382 A269383 A269384 * A269386 A269387 A269388

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 01 2016

Status

approved