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Numbers k that A064413(k) = k.
9

%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