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1, 4, 12, 2, 32, 8, 84, 6, 19, 24, 220, 3, 18, 50, 63, 53, 564, 13, 9, 138, 49, 128, 162, 10, 31, 136, 38, 365, 1448, 36, 25, 5, 351, 126, 332, 30, 414, 27, 81, 82, 348, 99, 931, 103, 86, 3699, 96, 929, 21, 14, 64, 223, 16, 79, 892, 210, 325, 847, 80, 265, 1056, 72, 15, 51, 208, 212, 884, 221, 256
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OFFSET
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1,2
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COMMENTS
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Self-inverse permutation of natural numbers.
Shares with A088609 the property that after 1, positions indexed by squarefree numbers larger than one, A005117(n+1): 2, 3, 5, 6, 7, 10, 11, 13, 14, ... contain only nonsquarefree numbers A013929: 4, 8, 9, 12, 16, 18, 20, 24, ..., and vice versa. However, instead of placing terms in those subsets in monotone order this sequence recursively permutes the order of both subsets with the emerging permutation itself, thus implementing a kind of "deep" variant of A088609. Alternatively, this can be viewed as yet another "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case complementary pair A005117/A013929 is entangled with complementary pair A013929/A005117.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..520
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(1), and for n>1, if mu(n) = 0, a(n) = A005117(1+a(A057627(n))), otherwise, a(n) = A013929(a(A013928(n))). [Here mu is Moebius mu-function, A008683, which is zero only when n is a nonsquarefree number, one of the numbers in A013929.]
For all n > 1, A008966(a(n)) = 1 - A008966(n), or equally, mu(a(n)) + 1 = mu(n) modulo 2, where mu is Moebius mu (A008683). [Note: Permutation A088609 satisfies the same condition.]
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PROG
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(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A243347 n) (cond ((<= n 1) n) ((zero? (A008966 n)) (A005117 (+ 1 (A243347 (A057627 n))))) (else (A013929 (A243347 (A013928 n))))))
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CROSSREFS
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Cf. A008966, A005117, A013929, A013928, A057627, A088609, A243348.
Similar permutations: A236854, A235491, A243343-A243346, A243347, A243287-A243288, A135141-A227413, A237126-A237427, A193231.
Sequence in context: A016487 A104063 A260430 * A317555 A213343 A308518
Adjacent sequences: A243344 A243345 A243346 * A243348 A243349 A243350
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jun 03 2014
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STATUS
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approved
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