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A251604 A Zumkeller-type sequence (cf. A098550): a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common factor with a(n-2)+a(n-1), but none with a(n-1).

%I A251604 #30 Jul 31 2018 03:32:09
%S A251604 1,2,3,5,4,9,13,6,19,10,29,12,41,53,8,61,15,14,87,101,16,21,37,18,11,
%T A251604 58,23,24,47,71,20,7,27,17,22,39,122,35,157,26,33,59,28,45,73,30,103,
%U A251604 38,51,89,25,32,57,178,55,233,34,63,97,36,49,40,267,307,42
%N A251604 A Zumkeller-type sequence (cf. A098550): a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common factor with a(n-2)+a(n-1), but none with a(n-1).
%C A251604 Conjectured to be a permutation of the positive integers.
%C A251604 See also A255972 for this conjecture. - _Reinhard Zumkeller_, Mar 12 2015
%H A251604 Peter J. C. Moses, <a href="/A251604/b251604.txt">Table of n, a(n) for n = 1..5000</a>
%H A251604 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 A251604 a[n_] := a[n] = If[n <= 3, n, For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], If[!CoprimeQ[k, a[n-2]+a[n-1]] && CoprimeQ[k, a[n-1]], Return[k]]]]];
%t A251604 Array[a, 65] (* _Jean-François Alcover_, Jul 31 2018 *)
%o A251604 (Haskell)
%o A251604 import Data.List (delete)
%o A251604 a251604 n = a251604_list !! (n-1)
%o A251604 a251604_list = 1 : 2 : 3 : f 2 3 [4..] where
%o A251604    f u v ws = g ws where
%o A251604      g (x:xs) = if gcd x (u + v) > 1 && gcd x v == 1
%o A251604                    then x : f v x (delete x ws) else g xs
%o A251604 -- _Reinhard Zumkeller_, Mar 12 2015
%Y A251604 Cf. A098550.
%Y A251604 Cf. A255972.
%K A251604 nonn
%O A251604 1,2
%A A251604 _Vladimir Shevelev_, Dec 13 2014
%E A251604 More terms from _Peter J. C. Moses_, Dec 13 2014