A292766 - OEIS

%I #13 Sep 27 2017 13:28:28

%S 270,440,496,702,737,813,828,897,905,1027,1066,1099,1240,1241,1260,

%T 1331,1353,1368,1371,1422,1507,1537,1754,1760,1834,1848,2002,2016,2282

%N Numbers n whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded, excluding numbers n whose trajectory merges with the trajectory of a smaller number.

%C These are the "seeds" in A291790, that is, every number which blows up under iteration of the map k -> (sigma(k)+phi(k))/2 belongs to one of these trajectories. AT PRESENT ALL TERMS ARE CONJECTURAL.

%C The trajectories of these numbers are pairwise disjoint for the first 400 steps.

%C This is unsatisfactory because it is possible that, at some later step, these trajectories may merge, reach a prime (a fixed point), or reach a fraction (and die). However, this seems unlikely on probabilistic grounds - see the remarks of _Andrew R. Booker_ in A292108.

%C Normally such a sequence would not be included in the OEIS, but exceptions have been made for this and A291790 because a number of people have worked on them, and also in the hope that this will encourage resolution of some of the open questions.

%C Needs a b-file.

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

%Y Cf. A291790, A292108.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 27 2017, based on emails from _Sean A. Irvine_, Sep 14 2017, who computed a(1)-a(9), and _Hans Havermann_, same date, who computed a(10)-a(29). _Hugo Pfoertner_ also computed many of these terms.