A251411 - OEIS

%I #26 Jan 29 2025 13:09:26

%S 1,2,3,4,12,50,86

%N Numbers k such that A098550(k) = k.

%C There is a strong conjecture that there are no further terms. See the discussion in the comments in A098550.

%D L. Edson Jeffery, Posting to Sequence Fans Mailing List, Nov 30 2014.

%H Hans Havermann, <a href="http://chesswanks.com/num/a098550loops&amp;chains.txt">Loops and unresolved chains for map n -> A098550(n) trajectories</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>.

%t max = 100;

%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 A098550 = Nest[f, {1, 2, 3}, max - 3];

%t Select[Transpose[{Range[max], A098550}], #[[1]] == #[[2]]&][[All, 1]] (* _Jean-François Alcover_, Sep 05 2018, after _Robert G. Wilson v_ in A098550 *)

%o (Python)

%o from math import gcd

%o A251411_list, l1, l2, s, b = [1,2,3], 3, 2, 4, {}

%o for n in range(4,10**4):

%o     i = s

%o     while True:

%o         if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:

%o             l2, l1, b[i] = l1, i, 1

%o             while s in b:

%o                 b.pop(s)

%o                 s += 1

%o             if i == n:

%o                 A251411_list.append(n)

%o             break

%o         i += 1 # _Chai Wah Wu_, Dec 03 2014

%Y Cf. A098550, A251412, A251556.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Dec 02 2014