OFFSET
1,4
COMMENTS
a(n) is unbounded by a theorem of Westzynthius. - Charles R Greathouse IV, Sep 04 2015
LINKS
Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, and Terence Tao, Long gaps between primes (2014).
FORMULA
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
EXAMPLE
a(217) = floor((1361-1327)/log(1327)) = floor(4.72834...) = 4.
MATHEMATICA
Table[Floor[(Prime[n+1]-Prime[n])/Log[Prime[n]]//N], {n, 1, 220}]
PROG
(PARI) a(n, p=prime(n))=(nextprime(p+1)-p)\log(p) \\ Charles R Greathouse IV, Sep 04 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 17 2003
STATUS
approved