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%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
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