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 A269385 Tree of Ludic sieve, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)). 7
 1, 2, 4, 3, 8, 9, 6, 5, 16, 21, 18, 19, 12, 15, 10, 7, 32, 45, 42, 49, 36, 51, 38, 31, 24, 33, 30, 35, 20, 27, 14, 11, 64, 93, 90, 109, 84, 123, 98, 85, 72, 105, 102, 125, 76, 111, 62, 55, 48, 69, 66, 79, 60, 87, 70, 59, 40, 57, 54, 65, 28, 39, 22, 13, 128, 189, 186, 229, 180, 267, 218, 191, 168, 249, 246, 305, 196, 291, 170, 151, 144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Permutation of natural numbers obtained from the Ludic sieve. Note the indexing: Domain starts from 0, range from 1. This sequence can be represented as a binary tree. Each left hand child is obtained by doubling the parent's contents, and each right hand child is obtained by applying A269379 to the parent's contents:                                      1                                      |                   ...................2...................                  4                                       3        8......../ \........9                   6......../ \........5       / \                 / \                 / \                 / \      /   \               /   \               /   \               /   \     /     \             /     \             /     \             /     \   16       21         18       19         12       15         10       7 32  45   42  49     36  51   38  31     24  33   30  35     20  27   14 11 etc. Sequence A269387 is obtained from the mirror image of the same tree. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8191 FORMULA a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)). As a composition of related permutations: a(n) = A269171(A252755(n)). a(n) = A260741(A269375(n)). Other identities. For all n >= 2: A000035(a(n)) = A000035(n). [This permutation preserves the parity of n from a(2)=4 onward.] PROG (Scheme, with memoization-macro definec) (definec (A269385 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269385 (/ n 2)))) (else (A269379 (A269385 (/ (- n 1) 2)))))) CROSSREFS Inverse: A269386. Cf. A000035, A269379. Cf. A003309 (right edge of the tree). Related or similar permutations: A163511, A260741, A269387, A269171. Cf. also A252755, A269375. Sequence in context: A269851 A284457 A182944 * A252755 A163511 A332817 Adjacent sequences:  A269382 A269383 A269384 * A269386 A269387 A269388 KEYWORD nonn,tabf AUTHOR Antti Karttunen, Mar 01 2016 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)