# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a291790 Showing 1-1 of 1 %I A291790 #32 Oct 09 2017 15:28:55 %S A291790 270,290,308,326,327,328,352,369,393,394,395,396,410,440,458,459,465, %T A291790 496,504,510,525,559,560,570,606,616,620,685,686,702,712,725,734,735, %U A291790 737,738,745,746,747,783,791,792,805,806,813,814,815,816,828 %N A291790 Numbers whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded. %C A291790 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 A291790 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 A291790 Hugo Pfoertner, Table of n, a(n) for n = 1..82 %H A291790 Sean A. Irvine, Showing how the initial portions of some of these trajectories merge %H A291790 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) %Y A291790 Cf. A000010, A000203, A289997, A290001, A291789 (the trajectory of 270), A291787, A292108. %Y A291790 For the "seeds" see A292766. %K A291790 nonn %O A291790 1,1 %A A291790 _N. J. A. Sloane_, Sep 03 2017 %E A291790 More terms from _Hugo Pfoertner_, Sep 03 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE