OFFSET
1,1
COMMENTS
It seems that the distribution of the ratios of consecutive prime gaps exhibits a quite symmetric pattern, in the sense that the relative frequency of each ratio is similar to that of the inverse of that ratio (at least for the first 2*10^5 primes). This is more clearly seen by mean of a histogram of the logarithm of the ratios which is nearly symmetric and nearly centered around zero (see link).
Integer part of 2, 1, 2, 1/2, 2, 1/2, 2, 3/2, 1/3, 3, 2/3, 1/2,.... - R. J. Mathar, Jun 26 2016
LINKS
EXAMPLE
For n = 1 we have (prime(3)-prime(2))/(prime(2)-prime(1))) = (5-3)/(3-2) = 2 and its integer part is 2: a(1) = 2.
For n = 4 we have (prime(6)-prime(5))/(prime(5)-prime(4))) = (13-11)/(11-7) = 1/2 an its integer part is 0: a(4) = 0.
MAPLE
MATHEMATICA
Table[Floor[(Prime[j+2]-Prime[j+1])/(Prime[j+1]-Prime[j])], {j, 1, 200}];
IntegerPart[#[[2]]/#[[1]]]&/@Partition[Differences[Prime[Range[200]]], 2, 1] (* Harvey P. Dale, Mar 07 2018 *)
PROG
(PARI) a(n) = (prime(n+2)-prime(n+1))\(prime(n+1)-prime(n)); \\ Michel Marcus, Jun 18 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Andres Cicuttin, Jun 17 2016
STATUS
approved