The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A291790 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A291790

Numbers whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded.
(history; published version)

#32 by N. J. A. Sloane at Mon Oct 09 15:28:55 EDT 2017

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approved

#31 by N. J. A. Sloane at Mon Oct 09 15:28:51 EDT 2017

LINKS

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)

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#30 by N. J. A. Sloane at Wed Sep 27 13:27:01 EDT 2017

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#29 by N. J. A. Sloane at Wed Sep 27 13:26:58 EDT 2017

CROSSREFS

For the "seeds" see A292766.

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#28 by N. J. A. Sloane at Mon Sep 25 17:33:35 EDT 2017

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#27 by N. J. A. Sloane at Mon Sep 25 17:33:32 EDT 2017

LINKS

Sean A. Irvine, <a href="/A291790/a291790.png">Showing how the initial portions of some of these trajectories merge</a>

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#26 by N. J. A. Sloane at Mon Sep 25 17:31:21 EDT 2017

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#25 by N. J. A. Sloane at Mon Sep 25 17:31:19 EDT 2017

COMMENTS

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 _Anfrew Andrew R. Booker_ in A292108. - N. J. A. Sloane, Sep 25 2017

CROSSREFS

Cf. A000010, A000203, A289997, A290001, A291789 (the trajectory of 270), A291787, A292108.

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#24 by N. J. A. Sloane at Mon Sep 25 17:30:20 EDT 2017

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#23 by N. J. A. Sloane at Mon Sep 25 17:30:17 EDT 2017

COMMENTS

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 conjecturalAT 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 integral and unbounded. This has not yet happened, although see the remarks of _Anfrew R. Booker_ in A292108. - N. J. A. Sloane, Sep 25 2017

STATUS

approved

editing