A255615 a(n) is the number of even A098550 terms less than 2*prime(n) but occurring after 2*prime(n).

0, 0, 0, 3, 1, 2, 1, 0, 0, 1, 3, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 3, 0, 0, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 0, 4, 3, 2, 2, 2, 0, 0, 4, 5, 1, 2, 1, 1, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 2, 4, 4, 1, 0, 0, 1, 1

Offset: 1

Author

Vladimir Shevelev, Feb 28 2015

Keywords

• nonn

Examples

			Let A=A098550. Let n=4, prime(4)=7, 2*prime(4)=14 = A(8). We have 2=A(2), 4=A(4), 6=A(10), 8=A(6), 10=A(16), 12=A(12). Thus 6,10 and 12 appear in A later than 14. So a(4)=3.
		

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 [math.NT], 2015.

Crossrefs

Cf. A098550, A000040.

Programs

Mathematica

terms = 87;
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[[pos+1 ;; 12 terms]], 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 28 2015