A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

1, 2, 3, 6, 5, 4, 11, 8, 9, 10, 7, 18, 21, 28, 15, 12, 17, 22, 19, 38, 13, 16, 35, 26, 41, 58, 55, 102, 29, 40, 23, 14, 33, 46, 43, 80, 37, 52, 75, 56, 25, 34, 31, 60, 69, 100, 51, 44, 81, 118, 115, 206, 109, 160, 203, 152, 57, 82, 79, 144, 45, 64, 27, 20, 65, 94, 91, 164, 85, 124, 159, 120, 73, 106, 103, 186, 149, 220, 111, 96, 49

Offset: 1

Author

Antti Karttunen, Mar 01 2016

Keywords

• nonn
• tabf

Comments

Permutation obtained from the Lucky sieve.

This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269372(n), when the parent node contains n:

1

|

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

3 6

5......../ \........4 11......../ \........8

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

9 10 7 18 21 28 15 12

17 22 19 38 13 16 35 26 41 58 55 102 29 40 23 14

etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A269373.

Cf. A000035, A001511, A003602, A255551, A269372.

Cf. also A269375, A269377 and also A249814, A269384.

Formula

a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

a(1) = 1, a(2n) = A269372(a(n)), a(2n+1) = (2*a(n+1))-1.

Other identities. For all n >= 0:

A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]