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A251621 Run lengths in A249943. 3
1, 1, 1, 1, 1, 1, 3, 1, 2, 4, 1, 1, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
REFERENCES
Bradley Klee, Posting to Sequence Fans Mailing List, Dec 07 2014
Vladimir Shevelev, Postings to Sequence Fans Mailing List, Dec 07, 10 and 11, 2014
LINKS
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7.
FORMULA
Connection with prime gaps: conjecturally, for n>=13, we have a(n) = A001223(n-5). - Vladimir Shevelev, Dec 07 2014
Bradley Klee noted that this conjecture and his conjectures in A251416 are equivalent. At least to one side, our conjecture could be deduced from Klee's conjectures by a simple induction. - Vladimir Shevelev, Dec 10 2014
As a corollary, we have an explicit conjectural formula for prime(n), n>=8, essentially based on A098550: prime(n) = 19 + sum{i=9,...,n}a(i+4). - Vladimir Shevelev, Dec 11 2014
EXAMPLE
From Vladimir Shevelev, Dec 11 2014: (Start)
For formula for prime(n):
1) n=8, prime(8) = 19;
2) n=9, prime(9) = 19 + a(13) = 19 + 4 = 23;
3) n=10, prime(10)= 19 + a(13) + a(14) = 23 + 6 = 29, etc.
(End)
MATHEMATICA
f[lst_] := 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}, 1000]; runningMax = Rest[FoldList[Max, -Infinity, #]]&; A249943 = runningMax[Take[Ordering[A098550], NestWhile[#+1&, 1, MemberQ[A098550, #] &] - 1]]; Length /@ Split[A249943] (* Jean-François Alcover, Sep 11 2017, using code from Robert G. Wilson v *)
PROG
(Haskell)
import Data.List (group)
a251621 n = a251621_list !! (n-1)
a251621_list = map length $ group a249943_list
CROSSREFS
Sequence in context: A331695 A245538 A080890 * A016468 A134839 A077581
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 06 2014
STATUS
approved

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Last modified May 24 06:10 EDT 2024. Contains 372772 sequences. (Running on oeis4.)