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A257798
Permutation of natural numbers: a(1) = 1; a(2n) = nontriangular(a(n)), a(2n+1) = triangular(1+a(n)), where triangular = A000217, nontriangular = A014132.
3
1, 2, 3, 4, 6, 5, 10, 7, 15, 9, 28, 8, 21, 14, 66, 11, 36, 20, 136, 13, 55, 35, 435, 12, 45, 27, 253, 19, 120, 77, 2278, 16, 78, 44, 703, 26, 231, 152, 9453, 18, 105, 65, 1596, 43, 666, 464, 95266, 17, 91, 54, 1081, 34, 406, 275, 32385, 25, 210, 135, 7381, 89, 3081, 2345, 2598060, 22, 153, 90, 3160, 53, 1035, 740, 248160, 33
OFFSET
1,2
COMMENTS
This sequence can be represented as a binary tree. Each left hand child is produced as A014132(n) and each right hand child as A000217(1+n), when a parent contains n >= 1:
1
................../ \..................
2 3
4......../ \........6 5......../ \.......10
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
7 15 9 28 8 21 14 66
11 36 20 136 13 55 35 435 12 45 27 253 19 120 77 2278
etc.
FORMULA
a(1)=1; after which: a(2n) = A014132(a(n)), a(2n+1) = A000217(a(n)+1).
PROG
(Scheme, with memoizing definec-macro)
(definec (A257798 n) (cond ((<= n 1) n) ((even? n) (A014132 (A257798 (/ n 2)))) (else (A000217 (+ 1 (A257798 (/ (- n 1) 2)))))))
CROSSREFS
Inverse: A257797.
Cf. also permutation A183079.
Sequence in context: A064275 A080998 A209268 * A183079 A374797 A119629
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 18 2015
STATUS
approved