A291790 Numbers whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded.

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

Offset: 1

Author

N. J. A. Sloane, Sep 03 2017

Keywords

• nonn

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 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

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..82
• Sean A. Irvine, Showing how the initial portions of some of these trajectories merge
• 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)

Crossrefs

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

For the "seeds" see A292766.

Extensions

More terms from Hugo Pfoertner, Sep 03 2017