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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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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

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)

PROG

(Haskell)

import Data.List (group)

a251621 n = a251621_list !! (n-1)

a251621_list = map length $ group a249943_list

CROSSREFS

Cf. A000040, A001223, A098550, A249943, A251416, A251620.

Sequence in context: A262218 A245538 A080890 * A016468 A134839 A077581

Adjacent sequences:  A251618 A251619 A251620 * A251622 A251623 A251624

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 06 2014

STATUS

approved

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Last modified March 24 02:10 EDT 2017. Contains 283984 sequences.