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A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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.]

PROG

(Scheme, two different implementations, both using memoization-macro definec)

(definec (A269374 n) (cond ((<= n 1) n) (else (+ -1 (A255551bi (A001511 n) (A269374 (A003602 n))))))) ;; Code for A255551bi given in A255551.

(definec (A269374 n) (cond ((<= n 1) n) ((even? n) (A269372 (A269374 (/ n 2)))) (else (+ -1 (* 2 (A269374 (/ (+ n 1) 2)))))))

CROSSREFS

Inverse: A269373.

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

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

Sequence in context: A254117 A218890 A269373 * A137761 A100769 A023889

Adjacent sequences:  A269371 A269372 A269373 * A269375 A269376 A269377

KEYWORD

nonn,tabf

AUTHOR

Antti Karttunen, Mar 01 2016

STATUS

approved

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Last modified February 21 04:55 EST 2020. Contains 332086 sequences. (Running on oeis4.)