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A251411 Numbers k such that A098550(k) = k.

%I A251411 #26 Jan 29 2025 13:09:26
%S A251411 1,2,3,4,12,50,86
%N A251411 Numbers k such that A098550(k) = k.
%C A251411 There is a strong conjecture that there are no further terms. See the discussion in the comments in A098550.
%D A251411 L. Edson Jeffery, Posting to Sequence Fans Mailing List, Nov 30 2014.
%H A251411 Hans Havermann, <a href="http://chesswanks.com/num/a098550loops&amp;chains.txt">Loops and unresolved chains for map n -> A098550(n) trajectories</a>
%H A251411 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 A251411 max = 100;
%t A251411 f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t A251411 A098550 = Nest[f, {1, 2, 3}, max - 3];
%t A251411 Select[Transpose[{Range[max], A098550}], #[[1]] == #[[2]]&][[All, 1]] (* _Jean-François Alcover_, Sep 05 2018, after _Robert G. Wilson v_ in A098550 *)
%o A251411 (Python)
%o A251411 from math import gcd
%o A251411 A251411_list, l1, l2, s, b = [1,2,3], 3, 2, 4, {}
%o A251411 for n in range(4,10**4):
%o A251411     i = s
%o A251411     while True:
%o A251411         if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
%o A251411             l2, l1, b[i] = l1, i, 1
%o A251411             while s in b:
%o A251411                 b.pop(s)
%o A251411                 s += 1
%o A251411             if i == n:
%o A251411                 A251411_list.append(n)
%o A251411             break
%o A251411         i += 1 # _Chai Wah Wu_, Dec 03 2014
%Y A251411 Cf. A098550, A251412, A251556.
%K A251411 nonn,more
%O A251411 1,2
%A A251411 _N. J. A. Sloane_, Dec 02 2014