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A321012 Trajectory of 596 under repeated application of the map k -> A320486(k^2). 5
596, 3216, 103425, 197325, 897162, 652, 2510, 631, 3986, 596, 3216, 103425, 197325, 897162, 652, 2510, 631, 3986, 596, 3216, 103425, 197325, 897162, 652, 2510, 631, 3986, 596, 3216, 103425, 197325, 897162, 652, 2510, 631, 3986, 596, 3216, 103425, 197325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

k -> A320486(k) is Eric Angelini's remove-repeated-digits map.

Lars Blomberg has discovered that if we start with any positive integer and repeatedly apply the map k -> A320486(k^2) then we will eventually either:

- reach 0,

- reach one of the four fixed points 1, 1465, 4376, 89476 (see A321010)

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

- reach the period-9 cycle shown in A321012.

Since there are only finitely many possible starting values with all digits distinct, it should not be difficult to check that this is true (and indeed, Lars Blomberg may by now have completed the proof).

REFERENCES

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

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

FORMULA

From Colin Barker, Nov 04 2018: (Start)

G.f.: x*(596 + 3216*x + 103425*x^2 + 197325*x^3 + 897162*x^4 + 652*x^5 + 2510*x^6 + 631*x^7 + 3986*x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)).

a(n) = a(n-9) for n>9.

(End)

EXAMPLE

The cycle of length 9 is (596, 3216, 103425, 197325, 897162, 652, 2510, 631, 3986).

PROG

(PARI) Vec(x*(596 + 3216*x + 103425*x^2 + 197325*x^3 + 897162*x^4 + 652*x^5 + 2510*x^6 + 631*x^7 + 3986*x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^40)) \\ Colin Barker, Nov 04 2018

CROSSREFS

Cf. A320485, A320486, A321010, A321011.

Sequence in context: A252534 A249705 A197647 * A238034 A293098 A160149

Adjacent sequences:  A321009 A321010 A321011 * A321013 A321014 A321015

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, Nov 04 2018

STATUS

approved

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)