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A268712
Permutation of natural numbers: a(1) = 1, a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).
4
1, 2, 3, 6, 4, 9, 5, 13, 11, 10, 7, 21, 18, 12, 8, 29, 23, 25, 20, 24, 19, 14, 15, 45, 40, 39, 34, 28, 22, 17, 16, 62, 56, 49, 42, 54, 48, 44, 37, 51, 47, 43, 36, 30, 26, 33, 27, 95, 87, 84, 75, 80, 74, 73, 65, 61, 53, 46, 41, 38, 32, 35, 31, 129, 120, 115, 108, 100, 93, 88, 82, 112, 105, 99, 92, 94, 86, 78, 70
OFFSET
1,2
COMMENTS
This sequence can be represented as a binary tree. Each left hand child is produced as A268677(n), and each right hand child as A268678(1+n), when the parent node contains n:
|
...................1...................
2 3
6......../ \........4 9......../ \........5
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
13 11 10 7 21 18 12 8
29 23 25 20 24 19 14 15 45 40 39 34 28 22 17 16
etc.
FORMULA
a(1) = 1, after which: a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).
PROG
(Scheme, with memoization-macro definec)
(definec (A268712 n) (cond ((= 1 n) n) ((even? n) (A268677 (A268712 (/ n 2)))) (else (A268678 (+ 1 (A268712 (/ (- n 1) 2)))))))
CROSSREFS
Inverse: A268711.
Sequence in context: A101369 A125147 A103864 * A152679 A232561 A348395
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Feb 11 2016
STATUS
approved