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.
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
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