A082886 floor((prime(n+1)-prime(n))/log(prime(n))).

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

Offset: 1

Author

Labos Elemer, Apr 17 2003

Keywords

• nonn

Comments

a(n) is unbounded by a theorem of Westzynthius. - Charles R Greathouse IV, Sep 04 2015

Examples

			a(217) = floor((1361-1327)/log(1327)) = floor(4.72834...) = 4.
		

Links

• Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, and Terence Tao, Long gaps between primes (2014).

Crossrefs

Cf. A082862, A082884, A082885, A082888-A082891.

Programs

Mathematica

Table[Floor[(Prime[n+1]-Prime[n])/Log[Prime[n]]//N], {n, 1, 220}]

PARI

a(n,p=prime(n))=(nextprime(p+1)-p)\log(p) \\ Charles R Greathouse IV, Sep 04 2015

Formula

a(n)=floor((prime(n+1)-prime(n))/log(prime(n))).

a(n)=Floor(A001223(n)/log(A000040(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