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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.

LINKS

Table of n, a(n) for n=1..80.

Index entries for characteristic functions

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

AUTHOR

Rodolfo Ruiz-Huidobro, Jul 16 2018

STATUS

approved

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Last modified July 20 01:38 EDT 2019. Contains 325168 sequences. (Running on oeis4.)