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

0,1

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

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 *)

Prog

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

Crossrefs

Cf. A098550, A251411.

Sequence in context: A114167 A108302 A182689 * A286279 A125868 A240895

Adjacent sequences: A251409 A251410 A251411 * A251413 A251414 A251415

Keyword

nonn

Author

N. J. A. Sloane, Dec 02 2014

Status

approved