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

9, 9, 9, 9, 15, 15, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 27, 27, 33, 33, 33, 33, 33, 45, 45, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 57, 57, 57, 57, 57, 57, 57, 69, 69, 75, 75, 75, 75, 75, 75, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 105, 105, 105

Offset: 1

Author

N. J. A. Sloane, Dec 23 2014

Keywords

• nonn

Links

• Reinhard Zumkeller, 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 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550, A251542, A251546, A251557, A251559.

Cf. A014076.

Programs

Haskell

import Data.List (delete); import Data.List.Ordered (minus)
a251558 n = a251558_list !! (n-1)
a251558_list = 9 : 9 : 9 : f 2 3 [4..] (tail a014076_list) where
   f u v ws zs = g ws where
     g (x:xs) = if gcd x u > 1 && gcd x v == 1
                   then y : f v x (delete x ws) ys else g xs
                where ys@(y:_) = zs `minus` [x]
-- Reinhard Zumkeller, Mar 11 2015

Mathematica

terms = 70; max = 2 terms;
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;
A251542 = A098550[[sel]]/A098550[[sel-2]] ;
a[n_] := For[k = 1, k <= max, k = k+2, If[CompositeQ[k] && FreeQ[A098550[[1 ;; n]], k] && FreeQ[A251542, k], Return[k]]];
Table[a[n], {n, 1, terms}] (* Jean-François Alcover, Dec 06 2018, after Robert G. Wilson v in A098550 *)