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A082886
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floor((prime(n+1)-prime(n))/log(prime(n))).
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5
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1, 1, 1, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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a(n)=floor((prime(n+1)-prime(n))/log(prime(n))).
Infinitely often a(n) >> log log n log log log log n/log log log n, see Ford-Green-Konyagin-Maynard-Tao. - Charles R Greathouse IV, Sep 04 2015
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EXAMPLE
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a(217) = floor((1361-1327)/log(1327)) = floor(4.72834...) = 4.
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MATHEMATICA
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Table[Floor[(Prime[n+1]-Prime[n])/Log[Prime[n]]//N], {n, 1, 220}]
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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