A254669 Consider A098550(x_n)=2*prime(n). Let a(n) be number of even numbers<=2*prime(n) in A098550 in positions <=x_n.

2, 3, 5, 4, 10, 11, 16, 19, 23, 28, 28, 36, 40, 40, 46, 52, 58, 60, 67, 70, 72, 76, 83, 89, 97, 99, 102, 107, 108, 113, 126, 129, 136, 137, 149, 151, 155, 163, 167, 172, 177, 180, 190, 193, 197, 199, 207, 220, 225, 227, 231, 239, 241, 247, 252, 262, 267, 270

Offset: 1

Author

Vladimir Shevelev, Feb 04 2015

Keywords

• nonn

Comments

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

Examples

			Let n=10, p_n=29, 2*p_n=58, 58=A098550(63).
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.
We have 28 such numbers. Thus a(10)=28.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000
• 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.

Crossrefs

Cf. A098550.

Programs

Mathematica

terms = 58;
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];
a[n_] := Module[{p, pos}, p = Prime[n]; pos = FirstPosition[A098550, 2 p][[1]]; Count[A098550[[1 ;; pos]], k_ /; EvenQ[k] && k <= 2 p]];
Array[a, terms] (* Jean-François Alcover, Dec 12 2018, after Robert G. Wilson v in A098550 *)

Extensions

More terms from Peter J. C. Moses, Feb 04 2015