OFFSET
1,2
COMMENTS
The conjecture that all terms are positive is equivalent to the known conjecture that A098550 is a permutation of the positive integers.
Partial maxima of A098551: a(n) = max{a(n-1),A098551(n)} for n > 1. - Reinhard Zumkeller, Dec 06 2014
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, 2015 and J. Int. Seq. 18 (2015) 15.6.7.
FORMULA
The author conjectures that a(n)/n <= a(19)/19 = 43/19. Peter J. C. Moses verified that the strict inequality holds for 19 < n <= 1.1*10^5. - Vladimir Shevelev, Dec 06 2014
EXAMPLE
MATHEMATICA
f[lst_List] := 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}, 100]; runningMax := Rest[FoldList[Max, -Infinity, #]]&; runningMax[Take[Ordering[A098550], NestWhile[#+1&, 1, MemberQ[A098550, #]&]-1]] (* Jean-François Alcover, Dec 05 2014, after Robert G. Wilson v and Peter J. C. Moses *)
PROG
(Haskell)
a249943 n = a249943_list !! (n-1)
a249943_list = scanl1 max $ map a098551 [1..]
-- Reinhard Zumkeller, Dec 06 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 04 2014
STATUS
approved