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 A251554 a(1)=1, a(2)=2, a(3)=5; thereafter a(n) is the smallest number not occurring earlier having at least one common factor with a(n-2), but none with a(n-1). 3
 1, 2, 5, 4, 15, 8, 3, 10, 9, 14, 27, 7, 6, 35, 12, 25, 16, 45, 22, 21, 11, 18, 55, 24, 65, 28, 13, 20, 39, 32, 33, 26, 51, 38, 17, 19, 34, 57, 40, 63, 44, 49, 30, 77, 36, 91, 46, 105, 23, 42, 115, 48, 85, 52, 75, 56, 69, 50, 81, 58, 93, 29, 31, 87, 62, 99, 64, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A variant of A098550. See that entry for much more information. It seems likely that this sequence will never merge with A098550, but it would be nice to have a proof. LINKS Chai Wah Wu, 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, 2015 and J. Int. Seq. 18 (2015) 15.6.7. MATHEMATICA a251554[lst_List] := Block[{k = 3},   While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 ||     MemberQ[lst, k], k++]; Append[lst, k]]; Nest[a251554, {1, 2, 5}, 120] (* Michael De Vlieger, Dec 23 2014, after Robert G. Wilson v at A098850 *) PROG (Python) from fractions import gcd A251554_list, l1, l2, s, b = [1, 2, 5], 5, 2, 3, {5} for _ in range(10**4): ....i = s ....while True: ........if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1: ............A251554_list.append(i) ............l2, l1 = l1, i ............b.add(i) ............while s in b: ................b.remove(s) ................s += 1 ............break ........i += 1 # Chai Wah Wu, Dec 21 2014 (Haskell) import Data.List (delete) a251554 n = a251554_list !! (n-1) a251554_list = 1 : 2 : 5 : f 2 5 (3 : 4 : [6..]) where    f u v ws = g ws where      g (x:xs) = if gcd x u > 1 && gcd x v == 1                    then x : f v x (delete x ws) else g xs -- Reinhard Zumkeller, Dec 26 2014 CROSSREFS Cf. A098550, A251555. Sequence in context: A079053 A224272 A189942 * A002518 A093727 A286146 Adjacent sequences:  A251551 A251552 A251553 * A251555 A251556 A251557 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 21 2014 STATUS approved

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Last modified July 19 01:02 EDT 2018. Contains 312766 sequences. (Running on oeis4.)