Conjecture: This sequence is finite.
Contribution from Artur Jasinski, Dec 08 2008: (Start)
The EKG sequence A064413 has 3 critical lines.
Numbers which belong to the critical lines:
(1) A064413(n)=n see A152458,
(3/2) 2*A064413(n)=3n see A152519,
(1/2) 2*A064413(n)=n has only 2 numbers {10, 14}.
Because points are concentrated on the plot of EKG sequence near these 3 critical lines, the number of points belonging to critical lines is surprisingly low.
Is this sequence complete? (End)
Also fixed points of A247379.  Reinhard Zumkeller, Sep 15 2014
