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A251542 List of values A098550(n+2)/A098550(n) for those n for which A098550(n) is a prime. 8

%I

%S 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 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 5,3,5,5,5,5,7,3,7,5,5,7,3,5,5,3,3,5,3,7,7,5

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

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

%C For n > 4: third column in A251715. - _Reinhard Zumkeller_, Dec 16 2014

%C a(n) <= 19 for n <= 10^6. - _Chai Wah Wu_, Dec 16 2014

%H Chai Wah Wu, <a href="/A251542/b251542.txt">Table of n, a(n) for n = 1..10000</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 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.

%e 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 max = 1200;

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

%t A098550 = Nest[f, {1, 2, 3}, max - 3];

%t sel = Select[Transpose[{Range[max], A098550}], PrimeQ[#[[2]]]&][[All,1]]+2;

%t A098550[[sel]]/A098550[[sel - 2]] (* _Jean-Fran├žois Alcover_, Sep 05 2018, after _Robert G. Wilson v_ in A098550 *)

%o (Haskell)

%o a251542 n = a251542_list !! (n-1)

%o a251542_list = [div u v | (u, v) <- zip(drop 2 a098550_list) a098550_list,

%o a010051' v == 1]

%o -- _Reinhard Zumkeller_, Mar 11 2015

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

%Y Cf. A251715.

%K nonn

%O 1,1

%A _David Applegate_ and _N. J. A. Sloane_, Dec 15 2014

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Last modified February 23 15:00 EST 2020. Contains 332166 sequences. (Running on oeis4.)