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A291789 Trajectory of 270 under repeated application of k -> (phi(k)+sigma(k))/2. 7
270, 396, 606, 712, 851, 852, 1148, 1416, 2032, 2488, 2960, 4110, 5512, 6918, 8076, 10780, 16044, 23784, 33720, 55240, 73230, 97672, 118470, 169840, 247224, 350260, 442848, 728448, 1213440, 2124864, 4080384, 8159616, 13515078, 15767596, 18626016, 29239504, 39012864, 62623600, 92580308 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The ultimate fate of this trajectory is presently unknown. It may reach a fractional value (when it dies), it may reach a prime (which would be a fixed point), it may enter a cycle of length greater than 1, or it may be unbounded. - Hugo Pfoertner and N. J. A. Sloane, Sep 18 2017

LINKS

Sean A. Irvine, Table of n, a(n) for n = 0..515 [Terms through a(250) from Hugo Pfoertner, terms a(251)-a(356) from N. J. A. Sloane]

Sean A. Irvine, Illustration of A291789 showing a(n+1)/a(n) (red), cumulative mean of a(n+1)/a(n) (green), and power of 2 in a(n) (blue)

Hugo Pfoertner, Illustration of A291789 using a recursive 5th order Butterworth filter with normalized cut-off frequency of 0.1 (0.5<->Nyquist frequency) to smooth the data.

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

MAPLE

orbit:= proc(n, m) uses numtheory;

  local V, k;

  V:= Vector(m);

  V[1]:= n;

  for k from 2 to m do V[k]:= (sigma(V[k-1])+ phi(V[k-1]))/2 od:

  convert(V, list)

end proc:

orbit(270, 200); # Robert Israel, Sep 07 2017

MATHEMATICA

NestWhileList[If[! IntegerQ@ #, -1/2, (DivisorSigma[1, #] + EulerPhi@ #)/2] &, 270, Nor[! IntegerQ@ #, SameQ@ ##] &, 2, 38] (* Michael De Vlieger, Sep 19 2017 *)

CROSSREFS

Cf. A000010, A000203, A289997, A290001, A291790, A291787, A291804, A291805.

See A291914 and A292108 for the "big picture".

Sequence in context: A025393 A291790 A025394 * A292766 A180151 A278130

Adjacent sequences:  A291786 A291787 A291788 * A291790 A291791 A291792

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 03 2017

STATUS

approved

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)