|
|
A321010
|
|
Numbers k such that f(k^2) = k, where f is Eric Angelini's remove-repeated-digits map x->A320486(x).
|
|
2
|
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
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:
- reach 0,
- reach one of the four fixed points 1, 1465, 4376, 89476 (this sequence),
- reach the period-10 cycle shown in A321011, or
- reach the period-9 cycle shown in A321012.
Verified by testing all possible 8877690 start values that these are the only fixed points and cycles.
Detailed counts are:
- 561354 reach 0,
- 963738 reach one of the four fixed points 1, 1465, 4376, 89476 (counts 946109, 434, 17065, 130),
- 7271337 reach the period-10 cycle, and
- 81261 reach the period-9 cycle. (End)
|
|
REFERENCES
|
Eric Angelini, Postings to Sequence Fans Mailing List, Oct 24 2018 and Oct 26 2018.
|
|
LINKS
|
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,fini
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|