%I #17 Aug 02 2018 11:54:57

%S 2,4,4,6,6,10,10,16,16,16,16,16,16,18,18,18,18,22,22,24,24,24,24,24,

%T 28,28,30,30,34,34,34,34,34,34,36,36,38,38,38,38,40,40,40,44,44,46,46,

%U 46,46,52,52,52,52,54,54,54,54,58,58,64,64,64,64,64,66,66,70,70,70,70,70,70,70

%N a(n) = 2 more than the largest even number among {A098550(1), A098550(2), ..., A098550(n)}.

%H Reinhard Zumkeller, <a href="/A251557/b251557.txt">Table of n, a(n) for n = 1..10000</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 [math.NT], 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.

%t terms = 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}, terms - 3];

%t a[1] = 2; a[n_] := Max[Select[A098550[[1 ;; n]], EvenQ]] + 2;

%t Array[a, terms] (* _Jean-François Alcover_, Aug 02 2018, after _Robert G. Wilson v_ *)

%o (Haskell)

%o a251557 n = a251557_list !! (n-1)

%o a251557_list = map (+ 2) $ tail $ scanl maxEven 0 a098550_list

%o where maxEven u v = if even v then max u v else u

%o -- _Reinhard Zumkeller_, Mar 10 2015

%Y Cf. A098550, A251546, A251558, A251559.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 23 2014