A269375 Tree of Lucky sieve, mirrored: a(0) = 1, a(1) = 2; after which a(2n) = 2*a(n), a(2n+1) = A269369(a(n)).

1, 2, 4, 3, 8, 5, 6, 7, 16, 17, 10, 19, 12, 11, 14, 9, 32, 41, 34, 61, 20, 23, 38, 27, 24, 29, 22, 39, 28, 35, 18, 13, 64, 89, 82, 145, 68, 95, 122, 91, 40, 53, 46, 81, 76, 107, 54, 45, 48, 65, 58, 103, 44, 59, 78, 57, 56, 77, 70, 123, 36, 47, 26, 15, 128, 185, 178, 313, 164, 239, 290, 217, 136, 197, 190, 333, 244, 359, 182, 147, 80

Offset

0,2

Comments

Permutation of natural numbers obtained from the Lucky 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 A269369 to the parent's contents:

1

|

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

4 3

8......../ \........5 6......../ \........7

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

16 17 10 19 12 11 14 9

32 41 34 61 20 23 38 27 24 29 22 39 28 35 18 13

etc.

Sequence A269377 is obtained from the mirror image of the same tree.

Links

Antti Karttunen, Table of n, a(n) for n = 0..4095

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) = A269369(a(n)).

As a composition of related permutations:

a(n) = A260742(A269385(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 (A269375 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269375 (/ n 2)))) (else (A269369 (A269375 (/ (- n 1) 2))))))

Crossrefs

Inverse: A269376.

Cf. A000035, A269369.

Cf. A000959 (with 2 inserted between 1 and 3 forms the right edge of the tree).

Related or similar permutations: A163511, A260742, A269377.

Cf. also A252755, A269385.

Sequence in context: A048167 A207790 A305427 * A135141 A098709 A054238

Adjacent sequences: A269372 A269373 A269374 * A269376 A269377 A269378

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 01 2016

Status

approved