login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321011 Trajectory of 86 under repeated application of the map k -> A320486(k^2). 3
86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723, 86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723, 86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723, 86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723 (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
FORMULA
From Colin Barker, Nov 04 2018: (Start)
G.f.: x*(86 + 7396*x + 547816*x^2 + 12985*x^3 + 805*x^4 + 648025*x^5 + 1325*x^6 + 1762*x^7 + 3106*x^8 + 94723*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-10) for n>10.
(End)
EXAMPLE
The cycle of length 10 is (86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723).
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723}, 40] (* or *) PadRight[ {}, 40, {86, 7396, 547816, 12985, 805, 648025, 1325, 1762, 3106, 94723}] (* Harvey P. Dale, Nov 05 2020 *)
PROG
(PARI) Vec(x*(86 + 7396*x + 547816*x^2 + 12985*x^3 + 805*x^4 + 648025*x^5 + 1325*x^6 + 1762*x^7 + 3106*x^8 + 94723*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^40)) \\ Colin Barker, Nov 04 2018
CROSSREFS
Sequence in context: A223828 A223786 A223972 * A093286 A093243 A223814
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Nov 04 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 22 19:08 EDT 2024. Contains 371906 sequences. (Running on oeis4.)