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

1,2

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

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

Prog

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

Crossrefs

Cf. A098550, A098551.

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

Sequence in context: A066105 A083180 A098551 * A251620 A128944 A295969

Adjacent sequences: A249940 A249941 A249942 * A249944 A249945 A249946

Keyword

nonn

Author

Vladimir Shevelev, Dec 04 2014

Status

approved