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A249943 a(n) = smallest k such that the numbers 1..n appear among A098550(1), ..., A098550(k), or a(n) = 0 if there is no such k. 6

%I

%S 1,2,3,4,9,10,15,15,15,16,22,22,23,23,23,23,30,31,43,43,43,43,51,51,

%T 51,51,51,51,61,61,62,62,62,62,62,62,79,79,79,79,87,87,88,88,88,88,101

%N a(n) = smallest k such that the numbers 1..n appear among A098550(1), ..., A098550(k), or a(n) = 0 if there is no such k.

%C The conjecture that all terms are positive is equivalent to the known conjecture that A098550 is a permutation of the positive integers.

%C Partial maxima of A098551: a(n) = max{a(n-1),A098551(n)} for n > 1. - _Reinhard Zumkeller_, Dec 06 2014

%H Reinhard Zumkeller, <a href="/A249943/b249943.txt">Table of n, a(n) for n = 1..10000</a>

%H 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, 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.

%F 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

%e Let n=6. Since A098550(9)=5 and A098550(10)=6, a(6)=10. - Corrected by _David Applegate_, Dec 08 2014

%t 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-Fran├žois Alcover_, Dec 05 2014, after _Robert G. Wilson v_ and _Peter J. C. Moses_ *)

%o (Haskell)

%o a249943 n = a249943_list !! (n-1)

%o a249943_list = scanl1 max $ map a098551 [1..]

%o -- _Reinhard Zumkeller_, Dec 06 2014

%Y Cf. A098550, A098551.

%Y Cf. A251620 (duplicates removed), A251621 (run lengths).

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Dec 04 2014

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)