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.

1, 2, 3, 4, 9, 10, 15, 15, 15, 16, 22, 22, 23, 23, 23, 23, 30, 31, 43, 43, 43, 43, 51, 51, 51, 51, 51, 51, 61, 61, 62, 62, 62, 62, 62, 62, 79, 79, 79, 79, 87, 87, 88, 88, 88, 88, 101

Offset: 1

Author

Vladimir Shevelev, Dec 04 2014

Keywords

• nonn

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

Examples

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

Crossrefs

Cf. A098550, A098551.

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

Programs

Haskell

a249943 n = a249943_list !! (n-1)
a249943_list = scanl1 max $ map a098551 [1..]
-- Reinhard Zumkeller, Dec 06 2014

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 *)

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