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 A316917 Let g(n) be the n-th maximal prime gap. a(n) = 1 if g(n) has record merit, 0 if it does not. 0
 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = 1 if A002386(n) is in A111870, a(n) = 0 if A002386(n) is not in A111870. A probable maximal gap of 1552 and merit 34.98 has been discovered (highly likely to be maximal). If it is verified as a maximal gap, we would have a(81) = 0. - Rodolfo Ruiz-Huidobro, Jun 22 2021 LINKS Prime Gap List Community, Record prime gaps, 2021. EXAMPLE The 5th record prime gap from 89 to 97 does not have record merit, so a(5) = 0. The 10th record prime gap from 1327 to 1361 has record merit, so a(10) = 1. MATHEMATICA Block[{nn = 10^6, s, t, u, v}, s = Prime@ Range[nn]; t = Differences@ s; u = Map[(#2 - #1)/Log[#1] & @@ # &, Partition[Prime@ Range[nn], 2, 1]]; v = Map[Prime@ FirstPosition[u, #][[1]] &, Union@ FoldList[Max, u]]; Boole[! FreeQ[v, s[[FirstPosition[t, #][[1]] ]] ] ] & /@ Union@ FoldList[Max, t]] (* Michael De Vlieger, Jul 19 2018 *) CROSSREFS Cf. A000101, A002386, A111870, A111871, A005250. Sequence in context: A115512 A115513 A133080 * A133985 A143062 A010815 Adjacent sequences:  A316914 A316915 A316916 * A316918 A316919 A316920 KEYWORD nonn,more AUTHOR Rodolfo Ruiz-Huidobro, Jul 16 2018 STATUS approved

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Last modified July 4 02:09 EDT 2022. Contains 355063 sequences. (Running on oeis4.)