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%I #13 Mar 17 2019 19:30:53
%S 5,8,13,22,38,65,112,193,334,578,1001,1733,3001,5197,9001,15590,27002,
%T 46768,81004,140303,243011,420907,729032,1262720,2187095,3788159,
%U 6561283,11364475,19683848,34093424,59051542,102280271,177154625,306840811,531463874
%N Trajectory of 5 under repeated application of x -> A306938(x).
%C Te Riele has shown this sequence increases for ever.
%H Amiram Eldar, <a href="/A306943/b306943.txt">Table of n, a(n) for n = 0..4190</a>
%H H. J. J. te Riele, <a href="https://ir.cwi.nl/pub/6662">Iteration of number-theoretic functions</a>, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example III.3.
%t f[n_] := If[Divisible[n, 3], n/3, Floor[n*Sqrt[3]]]; NestList[f, 5, 50] (* _Amiram Eldar_, Mar 17 2019 *)
%Y Cf. A306938, A306944.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Mar 17 2019
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