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A269864
Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).
5
1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 15, 16, 11, 26, 27, 28, 13, 12, 21, 22, 25, 36, 45, 46, 19, 14, 33, 76, 65, 66, 81, 82, 31, 18, 39, 34, 17, 56, 63, 64, 29, 50, 75, 106, 41, 116, 135, 136, 53, 24, 57, 40, 35, 86, 99, 226, 143, 120, 195, 196, 71, 206, 243, 244, 89, 38, 93, 52, 23, 96, 117, 100, 77, 20, 51, 166, 145, 156, 189, 190, 119, 32, 87
OFFSET
1,2
COMMENTS
This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains A269360(n) [= 1+A250469(n)] and the right hand child contains A250469(1+n):
1
|
................../ \..................
2 3
4......../ \........5 6......../ \........9
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
10 7 8 15 16 11 26 27
28 13 12 21 22 25 36 45 46 19 14 33 76 65 66 81
etc.
FORMULA
a(1) = 1, a(2n) = 1 + A250469(a(n)), a(2n+1) = A250469(1+a(n)).
PROG
(Scheme, with memoization-macro definec)
(definec (A269864 n) (cond ((= 1 n) 1) ((even? n) (+ 1 (A250469 (A269864 (/ n 2))))) (else (A250469 (+ 1 (A269864 (/ (- n 1) 2)))))))
CROSSREFS
Inverse: A269863.
Cf. also A269865, A269866, A269867.
Differs from similarly constructed A245606 for the first time at n=15, where a(15)=27 instead of 21.
Sequence in context: A269863 A297165 A245606 * A103681 A367696 A319824
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Mar 13 2016
STATUS
approved