A306938 - OEIS

%I #16 Mar 17 2019 19:33:48

%S 1,3,1,6,8,2,12,13,3,17,19,4,22,24,5,27,29,6,32,34,7,38,39,8,43,45,9,

%T 48,50,10,53,55,11,58,60,12,64,65,13,69,71,14,74,76,15,79,81,16,84,86,

%U 17,90,91,18,95,96,19,100,102,20,105,107,21,110,112,22

%N If n is divisible by 3 then a(n) = n/3 otherwise a(n) = floor(n*sqrt(3)).

%H Amiram Eldar, <a href="/A306938/b306938.txt">Table of n, a(n) for n = 1..10000</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. [Apparently the sequence is discussed earlier in the same volume on page 80, where it is proved that under certain conditions the iterates of this function go to infinity (namely, if there are two consecutive non-multiples of 3).]

%t a[n_] := If[Divisible[n, 3], n/3, Floor[n*Sqrt[3]]]; Array[a, 66] (* _Amiram Eldar_, Mar 17 2019 *)

%Y Cf. A306943, A306944.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 17 2019