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A321010 Numbers k such that f(k^2) = k, where f is Eric Angelini's remove-repeated-digits map x->A320486(x). 2
0, 1, 1465, 4376, 89476 (list; graph; refs; listen; history; text; internal format)
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.

From Lars Blomberg, Nov 17 2018: (Start)

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

Table of n, a(n) for n=1..5.

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

Cf. A320485, A320486, A321011, A321012.

Sequence in context: A284887 A237483 A280906 * A278368 A206862 A206956

Adjacent sequences:  A321007 A321008 A321009 * A321011 A321012 A321013

KEYWORD

nonn,base,fini

AUTHOR

N. J. A. Sloane, Nov 03 2018

STATUS

approved

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Last modified May 23 11:46 EDT 2022. Contains 353975 sequences. (Running on oeis4.)