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%I #36 Oct 03 2018 08:11:18
%S 11,25,26,45,95,78,105,203,196,267,455,424,392,555,498,440,406,376,
%T 340,785,1025,944,880,1119,1036,1363,1715,2097,2369,1097,1385,641,801,
%U 730,672,867,1077,1341,1238,1713,2091,971,1169,541,251,339,312,288,264,242,305,413,481,1115,1030,1247
%N Trajectory of 11 under the map n -> A098550(n).
%C It is believed that n -> A098550(n) is a permutation of the natural numbers. 1,2,3,4 are fixed points (cf. A251411), and there are cycles (5,9), (6,8,14,16,10), and (7,15). 11 is the smallest number whose trajectory is not presently known (and is probably infinite).
%C _Hans Havermann_ has found that 1470 is in a cycle of length 30, and 1772 is in a cycle of length 84.
%D Hans Havermann, Posting to Sequence Fans Mailing List, Dec 02 2014
%H Reinhard Zumkeller and Hans Havermann (Reinhard Zumkeller to 119), <a href="/A251412/b251412.txt">Table of n, a(n) for n = 0..700</a>
%H David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669, 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.
%H Hans Havermann, <a href="http://chesswanks.com/num/a098550loops&chains.txt">Loops and unresolved chains for map n -> A098550(n) trajectories</a>
%H Hans Havermann, <a href="/A251412/a251412.txt">A portion of the trajectory containing 11</a>
%t f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t ff = Nest[f, {1, 2, 3}, 2500];
%t g[n_ /; 1 <= n <= Length[ff]] := ff[[n]];
%t NestWhileList[g, 11, # <= Length[ff] &] (* _Jean-François Alcover_, Oct 03 2018, after _Robert G. Wilson v_ in A098550 *)
%o (Haskell)
%o a251412 n = a251412_list !! (n-1)
%o a251412_list = iterate a098550 11 -- _Reinhard Zumkeller_, Dec 07 2014
%Y Cf. A098550, A251411.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Dec 02 2014
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