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A251412 Trajectory of 11 under the map n -> A098550(n).

%I A251412 #36 Oct 03 2018 08:11:18
%S A251412 11,25,26,45,95,78,105,203,196,267,455,424,392,555,498,440,406,376,
%T A251412 340,785,1025,944,880,1119,1036,1363,1715,2097,2369,1097,1385,641,801,
%U A251412 730,672,867,1077,1341,1238,1713,2091,971,1169,541,251,339,312,288,264,242,305,413,481,1115,1030,1247
%N A251412 Trajectory of 11 under the map n -> A098550(n).
%C A251412 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 A251412 _Hans Havermann_ has found that 1470 is in a cycle of length 30, and 1772 is in a cycle of length 84.
%D A251412 Hans Havermann, Posting to Sequence Fans Mailing List, Dec 02 2014
%H A251412 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 A251412 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 A251412 Hans Havermann, <a href="http://chesswanks.com/num/a098550loops&amp;chains.txt">Loops and unresolved chains for map n -> A098550(n) trajectories</a>
%H A251412 Hans Havermann, <a href="/A251412/a251412.txt">A portion of the trajectory containing 11</a>
%t A251412 f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t A251412 ff = Nest[f, {1, 2, 3}, 2500];
%t A251412 g[n_ /; 1 <= n <= Length[ff]] := ff[[n]];
%t A251412 NestWhileList[g, 11, # <= Length[ff] &] (* _Jean-François Alcover_, Oct 03 2018, after _Robert G. Wilson v_ in A098550 *)
%o A251412 (Haskell)
%o A251412 a251412 n = a251412_list !! (n-1)
%o A251412 a251412_list = iterate a098550 11  -- _Reinhard Zumkeller_, Dec 07 2014
%Y A251412 Cf. A098550, A251411.
%K A251412 nonn
%O A251412 0,1
%A A251412 _N. J. A. Sloane_, Dec 02 2014