This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217218 #34 Jul 30 2025 19:41:42
%S A217218 44,66,99,74,111,83,62,93,70,105,79,59,44,66,99,74,111,83,62,93,70,
%T A217218 105,79,59,44,66,99,74,111,83,62,93,70,105,79,59,44,66,99,74,111,83,
%U A217218 62,93,70,105,79,59,44,66,99,74,111,83,62,93,70,105,79,59,44,66,99,74,111,83,62,93,70,105,79,59,44,66,99,74,111,83,62,93,70,105,79,59,44,66,99,74,111,83,62,93,70,105,79,59
%N A217218 Trajectory of 44 under the map k -> A006368(k).
%C A217218 Periodic with period length 12.
%C A217218 It is believed that this is the longest trajectory that cycles (the others are {1}, {2,3}, {4,6,9,7,5}).
%D A217218 See also references and links in A006368.
%H A217218 Colin Barker, <a href="/A217218/b217218.txt">Table of n, a(n) for n = 1..1000</a>
%H A217218 J. H. Conway, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.03.192">On unsettleable arithmetical problems</a>, Amer. Math. Monthly, 120 (2013), 192-198.
%H A217218 John L Simons, <a href="https://arxiv.org/abs/2205.10582">Cycles and divergent trajectories for a class of permutation sequences</a>, arXiv:2205.10582 [math.NT], 2022.
%H A217218 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).
%F A217218 a(n+1) = A006368(a(n)).
%F A217218 From _Colin Barker_, Aug 16 2019: (Start)
%F A217218 G.f.: x*(44 + 66*x + 99*x^2 + 74*x^3 + 111*x^4 + 83*x^5 + 62*x^6 + 93*x^7 + 70*x^8 + 105*x^9 + 79*x^10 + 59*x^11) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).
%F A217218 a(n) = a(n-12) for n>12.
%F A217218 (End)
%t A217218 t={44}; While[n=t[[-1]]; s=If[EvenQ[n], 3*n/2, Round[3*n/4]]; Length[t]<100&&!MemberQ[t, s], AppendTo[t, s]]; t (* _Vincenzo Librandi_, Jun 28 2015 *)
%t A217218 PadRight[{},120,{44,66,99,74,111,83,62,93,70,105,79,59}] (* _Harvey P. Dale_, Jul 30 2025 *)
%o A217218 (Haskell)
%o A217218 a217218 n = a217218_list !! (n-1)
%o A217218 a217218_list = iterate a006368 44 -- _Reinhard Zumkeller_, Apr 06 2013
%o A217218 (Magma) &cat[ [44,66,99,74,111,83,62,93,70,105,79,59]: n in [0..9] ]; // _Vincenzo Librandi_, Jun 28 2015
%o A217218 (PARI) Vec(x*(44 + 66*x + 99*x^2 + 74*x^3 + 111*x^4 + 83*x^5 + 62*x^6 + 93*x^7 + 70*x^8 + 105*x^9 + 79*x^10 + 59*x^11) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^40)) \\ _Colin Barker_, Aug 16 2019
%Y A217218 Cf. A006368.
%Y A217218 Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.
%K A217218 nonn,easy
%O A217218 1,1
%A A217218 _N. J. A. Sloane_, Oct 04 2012