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A291790
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Numbers whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded.
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9
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270, 290, 308, 326, 327, 328, 352, 369, 393, 394, 395, 396, 410, 440, 458, 459, 465, 496, 504, 510, 525, 559, 560, 570, 606, 616, 620, 685, 686, 702, 712, 725, 734, 735, 737, 738, 745, 746, 747, 783, 791, 792, 805, 806, 813, 814, 815, 816, 828
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OFFSET
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1,1
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COMMENTS
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It would be nice to have a proof that these trajectories are integral and unbounded, or, of course, that they eventually reach a fractional value (and die), or reach a prime (which is then a fixed point). (Cf. A291787.) If either of the last two things happen, then that value of n will be removed from the sequence. AT PRESENT ALL TERMS ARE CONJECTURAL.
When this sequence was submitted, there was a hope that it would be possible to prove that these trajectories were indeed integral and unbounded. This has not yet happened, although see the remarks of Andrew R. Booker in A292108. - N. J. A. Sloane, Sep 25 2017
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LINKS
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N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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