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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 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 *) 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.)