A321010 Numbers k such that f(k^2) = k, where f is Eric Angelini's remove-repeated-digits map x->A320486(x).

0, 1, 1465, 4376, 89476

Offset: 1

Author

N. J. A. Sloane, Nov 03 2018

Keywords

• nonn
• base
• fini

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

• 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.