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A008996 Increasing length runs of consecutive composite numbers (records). 9
1, 3, 5, 7, 13, 17, 19, 21, 33, 35, 43, 51, 71, 85, 95, 111, 113, 117, 131, 147, 153, 179, 209, 219, 221, 233, 247, 249, 281, 287, 291, 319, 335, 353, 381, 383, 393, 455, 463, 465, 473, 485, 489, 499, 513, 515, 531, 533, 539, 581, 587, 601, 651, 673, 715, 765 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: a(n) = O(n^2); specifically, a(n) <= n^2. - Alexei Kourbatov, Jan 23 2019
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 1..74 [taken from link below]
Jens Kruse Andersen, Maximal Prime Gaps
Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Thomas R. Nicely, New maximal prime gaps and first occurrences, Math. Comput. 68,227 (1999) 1311-1315.
Eric Weisstein's World of Mathematics, Prime Gaps
FORMULA
a(n) = A005250(n+1) - 1.
MATHEMATICA
maxGap = 1; Reap[ Do[ gap = Prime[n+1] - Prime[n]; If[gap > maxGap, Print[gap-1]; Sow[gap-1]; maxGap = gap], {n, 2, 10^8}]][[2, 1]] (* Jean-François Alcover, Jun 12 2013 *)
Module[{nn=10^8, cmps}, cmps=Table[If[CompositeQ[n], 1, {}], {n, nn}]; DeleteDuplicates[ Rest[ Length/@ Split[cmps]], GreaterEqual]] (* The program generates the first 24 terms of the sequnece. To generate more, increase the nn constant. *) (* Harvey P. Dale, Sep 04 2022 *)
PROG
(Haskell)
a008996 n = a008996_list !! (n-1)
a008996_list = 1 : f 0 (filter (> 1) $
map length $ group $ drop 3 a010051_list)
where f m (u : us) = if u <= m then f m us else u : f u us
-- Reinhard Zumkeller, Nov 27 2012
CROSSREFS
Sequence in context: A247458 A355424 A339501 * A261089 A264988 A031163
KEYWORD
nonn,nice
AUTHOR
Mark Cramer (m.cramer(AT)qut.edu.au), Mar 15 1996
EXTENSIONS
More terms from Warren D. Smith, Dec 11 2000
STATUS
approved

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)