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

11, 25, 26, 45, 95, 78, 105, 203, 196, 267, 455, 424, 392, 555, 498, 440, 406, 376, 340, 785, 1025, 944, 880, 1119, 1036, 1363, 1715, 2097, 2369, 1097, 1385, 641, 801, 730, 672, 867, 1077, 1341, 1238, 1713, 2091, 971, 1169, 541, 251, 339, 312, 288, 264, 242, 305, 413, 481, 1115, 1030, 1247

Offset: 0

Author

N. J. A. Sloane, Dec 02 2014

Keywords

• nonn

Comments

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).

Hans Havermann has found that 1470 is in a cycle of length 30, and 1772 is in a cycle of length 84.

References

• Hans Havermann, Posting to Sequence Fans Mailing List, Dec 02 2014

Links

• Reinhard Zumkeller and Hans Havermann (Reinhard Zumkeller to 119), Table of n, a(n) for n = 0..700
• David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015 and J. Int. Seq. 18 (2015) 15.6.7.
• Hans Havermann, Loops and unresolved chains for map n -> A098550(n) trajectories
• Hans Havermann, A portion of the trajectory containing 11

Crossrefs

Cf. A098550, A251411.

Programs

Haskell

a251412 n = a251412_list !! (n-1)
a251412_list = iterate a098550 11  -- Reinhard Zumkeller, Dec 07 2014

Mathematica

f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
ff = Nest[f, {1, 2, 3}, 2500];
g[n_ /; 1 <= n <= Length[ff]] := ff[[n]];
NestWhileList[g, 11, # <= Length[ff] &] (* Jean-François Alcover, Oct 03 2018, after Robert G. Wilson v in A098550 *)