%I #14 Dec 12 2018 03:17:02

%S 2,3,5,4,10,11,16,19,23,28,28,36,40,40,46,52,58,60,67,70,72,76,83,89,

%T 97,99,102,107,108,113,126,129,136,137,149,151,155,163,167,172,177,

%U 180,190,193,197,199,207,220,225,227,231,239,241,247,252,262,267,270

%N Consider A098550(x_n)=2*prime(n). Let a(n) be number of even numbers<=2*prime(n) in A098550 in positions <=x_n.

%C Conjecture. lim a(n)/prime(n)=1, as n goes to infinity.

%H Peter J. C. Moses, <a href="/A254669/b254669.txt">Table of n, a(n) for n = 1..1000</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.

%e Let n=10, p_n=29, 2*p_n=58, 58=A098550(63).

%e We consider all even terms <= 58 up to the position 63. They are 2,4,8,14,6,12,16,10,20,22,26,28,32,18,24,34,36,30,38,42,44,40,50,48,52,46,56,58.

%e We have 28 such numbers. Thus a(10)=28.

%t terms = 58;

%t f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k]>1 || MemberQ[lst, k], k++]; Append[lst, k]]; A098550 = Nest[f, {1, 2, 3}, 12 terms];

%t a[n_] := Module[{p, pos}, p = Prime[n]; pos = FirstPosition[A098550, 2 p][[1]]; Count[A098550[[1 ;; pos]], k_ /; EvenQ[k] && k <= 2 p]];

%t Array[a, terms] (* _Jean-François Alcover_, Dec 12 2018, after _Robert G. Wilson v_ in A098550 *)

%Y Cf. A098550.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Feb 04 2015

%E More terms from _Peter J. C. Moses_, Feb 04 2015