%I #22 Oct 23 2024 16:33:15
%S 1,2,8,40,64
%N Numbers k that A064413(k) = k.
%C Conjecture: This sequence is finite.
%C Contribution from _Artur Jasinski_, Dec 08 2008: (Start)
%C The EKG sequence A064413 has 3 critical lines.
%C Numbers which belong to the critical lines:
%C (1) A064413(k) = k see this sequence,
%C (3/2) 2*A064413(k) = 3*k see A152519,
%C (1/2) 2*A064413(k) = k has only 2 numbers {10, 14}.
%C 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.
%C Is this sequence complete? (End)
%C Also fixed points of A247379. - _Reinhard Zumkeller_, Sep 15 2014
%C a(6) > 10^5, if it exists. - _Amiram Eldar_, Oct 23 2024
%o (Haskell)
%o a152458 n = a152458_list !! (n-1)
%o a152458_list = [x | x <- [1..], a064413 x == x]
%o -- _Reinhard Zumkeller_, Sep 15 2014
%Y Cf. A064413, A152519, A247379.
%K nonn,more,changed
%O 1,2
%A _Artur Jasinski_, Dec 05 2008