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A257348
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Repeatedly applying the map x -> sigma(x) partitions the natural numbers into a number of disjoint trees; sequence gives the (conjectural) list of minimal representatives of these trees.
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6
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1, 2, 5, 16, 19, 27, 29, 33, 49, 50, 52, 66, 81, 85, 105, 146, 147, 163, 170, 189, 197, 199, 218, 226, 243, 262, 303, 315, 343, 424, 430, 438, 453, 461, 463, 469, 472, 484, 489, 513, 530, 550, 584, 677, 722, 746, 786, 787, 804, 813, 821, 831, 842, 859, 867, 876, 892, 903, 914, 916, 937, 977, 982, 988, 990, 1029
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OFFSET
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1,2
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COMMENTS
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Very little is known for certain. Even the trajectories of 2 (A007497) and 5 (A051572) under repeated application of the map x -> sigma(x) (cf. A000203) are only conjectured to be disjoint.
The thousand-term b-file (up to 141441) has been checked to correspond to disjoint trees for 265 iterations of sigma on each term, and every non-term n < 141441 merges (in at most 21 iterations) with an earlier iteration sequence. - Hans Havermann, Nov 22 2019
Rather than trees we mean connected components of the graphs with edges x -> sigma(x). The number 1 is a fixed point, i.e., a cycle of length 1 under iterations of sigma, it is not part of a tree. But since sigma(n) > n for n > 1 there are no other cycles. - M. F. Hasler, Nov 21 2019
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REFERENCES
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Kerry Mitchell, Posting to Math Fun Mailing List, Apr 30 2015
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LINKS
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CROSSREFS
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Cf. A216200 (number of disjoint trees up to n); A257669 and A257670: size and smallest number of subtree rooted in n.
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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