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

%I A251542 #30 Sep 05 2018 11:50:11
%S A251542 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,
%T A251542 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,
%U A251542 5,3,5,5,5,5,7,3,7,5,5,7,3,5,5,3,3,5,3,7,7,5
%N A251542 List of values A098550(n+2)/A098550(n) for those n for which A098550(n) is a prime.
%C A251542 a(n) <= 17 for n <= 250000 (see A251543).
%C A251542 For n > 4: third column in A251715. - _Reinhard Zumkeller_, Dec 16 2014
%C A251542 a(n) <= 19 for n <= 10^6. - _Chai Wah Wu_, Dec 16 2014
%H A251542 Chai Wah Wu, <a href="/A251542/b251542.txt">Table of n, a(n) for n = 1..10000</a>
%H A251542 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 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.
%e A251542 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,...
%t A251542 max = 1200;
%t A251542 f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t A251542 A098550 = Nest[f, {1, 2, 3}, max - 3];
%t A251542 sel = Select[Transpose[{Range[max], A098550}], PrimeQ[#[[2]]]&][[All,1]]+2;
%t A251542 A098550[[sel]]/A098550[[sel - 2]] (* _Jean-François Alcover_, Sep 05 2018, after _Robert G. Wilson v_ in A098550 *)
%o A251542 (Haskell)
%o A251542 a251542 n = a251542_list !! (n-1)
%o A251542 a251542_list = [div u v | (u, v) <- zip(drop 2 a098550_list) a098550_list,
%o A251542                           a010051' v == 1]
%o A251542 -- _Reinhard Zumkeller_, Mar 11 2015
%Y A251542 Cf. A098550, A251543. See A251544 for the actual values of A098550(n+2).
%Y A251542 Cf. A251715.
%K A251542 nonn
%O A251542 1,1
%A A251542 _David Applegate_ and _N. J. A. Sloane_, Dec 15 2014