A321010 - OEIS

%I #28 Jul 17 2021 11:23:30

%S 0,1,1465,4376,89476

%N Numbers k such that f(k^2) = k, where f is Eric Angelini's remove-repeated-digits map x->A320486(x).

%C _Lars Blomberg_ has discovered that if we start with any positive integer and repeatedly apply the map m -> A320486(m^2) then we will eventually either:

%C - reach 0,

%C - reach one of the four fixed points 1, 1465, 4376, 89476 (this sequence),

%C - reach the period-10 cycle shown in A321011, or

%C - reach the period-9 cycle shown in A321012.

%C From _Lars Blomberg_, Nov 17 2018: (Start)

%C Verified by testing all possible 8877690 start values that these are the only fixed points and cycles.

%C Detailed counts are:

%C - 561354 reach 0,

%C - 963738 reach one of the four fixed points 1, 1465, 4376, 89476 (counts 946109, 434, 17065, 130),

%C - 7271337 reach the period-10 cycle, and

%C - 81261 reach the period-9 cycle. (End)

%D Eric Angelini, Postings to Sequence Fans Mailing List, Oct 24 2018 and Oct 26 2018.

%H N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence)

%Y Cf. A320485, A320486, A321011, A321012.

%K nonn,base,fini

%O 1,3

%A _N. J. A. Sloane_, Nov 03 2018