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A269377
Tree of Lucky sieve: a(0) = 1, a(1) = 2; after which a(2n) = A269369(a(n)), a(2n+1) = 2*a(n).
6
1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 11, 12, 19, 10, 17, 16, 13, 18, 35, 28, 39, 22, 29, 24, 27, 38, 23, 20, 61, 34, 41, 32, 15, 26, 47, 36, 123, 70, 77, 56, 57, 78, 59, 44, 103, 58, 65, 48, 45, 54, 107, 76, 81, 46, 53, 40, 91, 122, 95, 68, 145, 82, 89, 64, 21, 30, 71, 52, 165, 94, 101, 72, 183, 246, 203, 140, 271, 154, 161, 112, 97
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. After a(1)=2, each left hand child is obtained by applying A269369 to the parent, and each right hand child is obtained by doubling the contents of the parent node, when the parent node contains n:
1
|
...................2...................
3 4
7......../ \........6 5......../ \........8
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
9 14 11 12 19 10 17 16
13 18 35 28 39 22 29 24 27 38 23 20 61 34 41 32
etc.
Sequence A269375 is obtained from the mirror image of the same tree.
FORMULA
a(0) = 1, a(1) = 2; after which, a(2n) = A269369(a(n)), a(2n+1) = 2*a(n).
As a composition of related permutations:
a(n) = A260742(A269387(n)).
PROG
(Scheme, with memoization-macro definec)
(definec (A269377 n) (cond ((<= n 2) (+ 1 n)) ((even? n) (A269369 (A269377 (/ n 2)))) (else (* 2 (A269377 (/ (- n 1) 2))))))
CROSSREFS
Inverse: A269378.
Cf. A269369.
Cf. A000959 (with 2 inserted between 1 and 3 forms the left edge of the tree).
Related permutation: A269375.
Cf. also A252753, A269387.
Sequence in context: A343601 A331275 A072028 * A072026 A332213 A235199
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Mar 01 2016
STATUS
approved