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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, On the nth record gap between primes in an arithmetic progression, arXiv:1709.05508 [math.NT], 2017; Int. Math. Forum, 13 (2018), 65-78.

Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

T. R. Nicely, List of prime gaps

T. R. Nicely, New maximal prime gaps and first occurrences, Math. Comput. 68,227 (1999) 1311-1315.

Eric Weisstein's World of Mathematics, Prime Gaps

Index entries for primes, gaps between

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-Fran├žois Alcover, Jun 12 2013 *)

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

Cf. A005250, A008950, A008995, A058320.

Cf. A010051, A046933.

Sequence in context: A246026 A188574 A247458 * A261089 A264988 A031163

Adjacent sequences:  A008993 A008994 A008995 * A008997 A008998 A008999

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 August 20 14:06 EDT 2019. Contains 326152 sequences. (Running on oeis4.)