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A251558 a(n) = smallest odd number not in {A098550(1), A098550(2), ..., A098550(n)} which is neither a prime nor a term of A251542.

%I A251558 #31 May 09 2021 02:28:40
%S A251558 9,9,9,9,15,15,21,21,21,21,21,21,21,21,21,21,27,27,33,33,33,33,33,45,
%T A251558 45,49,49,49,49,49,49,49,49,49,49,49,49,49,49,57,57,57,57,57,57,57,69,
%U A251558 69,75,75,75,75,75,75,77,77,77,77,77,77,77,77,77,77,77,77,77,105,105,105
%N A251558 a(n) = smallest odd number not in {A098550(1), A098550(2), ..., A098550(n)} which is neither a prime nor a term of A251542.
%H A251558 Reinhard Zumkeller, <a href="/A251558/b251558.txt">Table of n, a(n) for n = 1..10000</a>
%H A251558 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 [math.NT], 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.
%t A251558 terms = 70; max = 2 terms;
%t A251558 f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t A251558 A098550 = Nest[f, {1, 2, 3}, max-3];
%t A251558 sel = Select[Transpose[{Range[max], A098550}], PrimeQ[#[[2]]]&][[All,1]]+2;
%t A251558 A251542 = A098550[[sel]]/A098550[[sel-2]] ;
%t A251558 a[n_] := For[k = 1, k <= max, k = k+2, If[CompositeQ[k] && FreeQ[A098550[[1 ;; n]], k] && FreeQ[A251542, k], Return[k]]];
%t A251558 Table[a[n], {n, 1, terms}] (* _Jean-François Alcover_, Dec 06 2018, after _Robert G. Wilson v_ in A098550 *)
%o A251558 (Haskell)
%o A251558 import Data.List (delete); import Data.List.Ordered (minus)
%o A251558 a251558 n = a251558_list !! (n-1)
%o A251558 a251558_list = 9 : 9 : 9 : f 2 3 [4..] (tail a014076_list) where
%o A251558    f u v ws zs = g ws where
%o A251558      g (x:xs) = if gcd x u > 1 && gcd x v == 1
%o A251558                    then y : f v x (delete x ws) ys else g xs
%o A251558                 where ys@(y:_) = zs `minus` [x]
%o A251558 -- _Reinhard Zumkeller_, Mar 11 2015
%Y A251558 Cf. A098550, A251542, A251546, A251557, A251559.
%Y A251558 Cf. A014076.
%K A251558 nonn
%O A251558 1,1
%A A251558 _N. J. A. Sloane_, Dec 23 2014