A251542 List of values A098550(n+2)/A098550(n) for those n for which A098550(n) is a prime.

2, 3, 5, 3, 3, 2, 5, 5, 5, 2, 3, 3, 2, 3, 7, 5, 3, 7, 5, 3, 5, 3, 7, 3, 7, 5, 3, 3, 5, 5, 3, 5, 3, 7, 7, 5, 5, 7, 5, 3, 5, 7, 7, 3, 5, 3, 3, 5, 5, 3, 3, 7, 3, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 11, 3, 5, 5, 5, 3, 5, 5, 5, 5, 7, 3, 7, 5, 5, 7, 3, 5, 5, 3, 3, 5, 3, 7, 7, 5

Offset: 1

Author

David Applegate and N. J. A. Sloane, Dec 15 2014

Keywords

• nonn

Comments

a(n) <= 17 for n <= 250000 (see A251543).

For n > 4: third column in A251715. - Reinhard Zumkeller, Dec 16 2014

a(n) <= 19 for n <= 10^6. - Chai Wah Wu, Dec 16 2014

Examples

			A098550(n) for n= 1..11 is 1,2,3,4,9,8,15,14,5,6,25. Each time you see a prime, divide the term two steps ahead by that prime. The result is 4/2=2, 9/3=3, 25/5=5,...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• 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 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550, A251543. See A251544 for the actual values of A098550(n+2).

Cf. A251715.

Programs

Haskell

a251542 n = a251542_list !! (n-1)
a251542_list = [div u v | (u, v) <- zip(drop 2 a098550_list) a098550_list,
                          a010051' v == 1]
-- Reinhard Zumkeller, Mar 11 2015

Mathematica

max = 1200;
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}, max - 3];
sel = Select[Transpose[{Range[max], A098550}], PrimeQ[#[[2]]]&][[All,1]]+2;
A098550[[sel]]/A098550[[sel - 2]] (* Jean-François Alcover, Sep 05 2018, after Robert G. Wilson v in A098550 *)