A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 15, 18, 13, 20, 11, 10, 17, 26, 27, 34, 29, 44, 35, 30, 25, 38, 39, 48, 21, 32, 19, 12, 33, 50, 51, 64, 53, 80, 67, 58, 57, 86, 87, 108, 69, 104, 59, 54, 49, 74, 75, 94, 77, 116, 95, 84, 41, 62, 63, 78, 37, 56, 23, 16, 65, 98, 99, 124, 101, 152, 127, 112, 105, 158, 159, 198, 133, 200

Offset

1,2

Comments

Permutation obtained from the Ludic 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 A269382(n), when the parent node contains n:

1

|

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

3 4

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

9 14 15 18 13 20 11 10

17 26 27 34 29 44 35 30 25 38 39 48 21 32 19 12

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

a(1) = 1, a(2n) = A269382(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.]

Prog

(Scheme, two different implementations, both using memoization-macro definec)
(definec (A269384 n) (cond ((<= n 1) n) ((even? n) (A269382 (A269384 (/ n 2)))) (else (+ -1 (* 2 (A269384 (/ (+ n 1) 2)))))))
(definec (A269384 n) (cond ((<= n 1) n) (else (+ -1 (A255127bi (A001511 n) (A269384 (A003602 n))))))) ;; Code for A255127bi given in A255127.

Crossrefs

Inverse: A269383.

Cf. A000035, A001511, A003602, A255127, A269382.

Cf. also A269385, A269387 and also A249814, A269374.

Sequence in context: A249811 A246676 A246678 * A249814 A246684 A249812

Adjacent sequences: A269381 A269382 A269383 * A269385 A269386 A269387

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 01 2016

Status

approved