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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
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 (list; graph; refs; listen; history; text; internal format)
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.

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-Fran├žois 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 A174437

Adjacent sequences:  A249940 A249941 A249942 * A249944 A249945 A249946

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Dec 04 2014

STATUS

approved

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Last modified April 25 14:22 EDT 2017. Contains 285414 sequences.