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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. 9


%S 270,290,308,326,327,328,352,369,393,394,395,396,410,440,458,459,465,

%T 496,504,510,525,559,560,570,606,616,620,685,686,702,712,725,734,735,

%U 737,738,745,746,747,783,791,792,805,806,813,814,815,816,828

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

%C 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.

%C 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

%H Hugo Pfoertner, <a href="/A291790/b291790.txt">Table of n, a(n) for n = 1..82</a>

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

%H 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)

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

%Y For the "seeds" see A292766.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 03 2017

%E More terms from _Hugo Pfoertner_, Sep 03 2017

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Last modified March 4 23:13 EST 2021. Contains 341812 sequences. (Running on oeis4.)